Preprints of Brian H. Bowditch

Preprints of Brian H. Bowditch

Median algebras
Brian H. Bowditch
First draft: March 2022. Revised: March 2024. (280 pages) Abstract.
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Embedding median algebras in median metric spaces
Brian H. Bowditch
First draft, March 2022. Revised, April 2022. (12 pages) Abstract.
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A Cartan-Hadamard theorem for median metric spaces
Brian H. Bowditch
First draft December 2021. Revised, May 2023. (27 pages) Abstract.
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Bilipschitz triangulations of riemannian manifolds
Brian H. Bowditch
April 2020. (28 pages) Abstract.
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Quasiflats in coarse median spaces
Brian H. Bowditch
First Draft: June 2019. Revised: December 2022. (61 pages) Abstract.
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Convex hulls in coarse median spaces
Brian H. Bowditch
First draft: August 2018. Revised: October 2020. (36 pages) Abstract.
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Limit sets of coarse embeddings
Brian H. Bowditch
July 2017. (8 pages) Abstract.
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The ending lamination theorem
Brian H. Bowditch
First draft, September 2011. Revised, January 2023 (205 pages) Abstract
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Coarse hyperbolic models for 3-manifolds
Brian H. Bowditch
September 2010. (34 pages) Abstract.
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Surface group actions and length bounds
Brian H. Bowditch
September 2010. (36 pages) Abstract.
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Train tracks and surface groups acting on hyperbolic spaces
Brian H. Bowditch
September 2010. (29 pages) Abstract.
[Download dvi (70K)] [Download pdf (290K)]

Notes on Maskit's planarity theorem
Brian H. Bowditch
First draft: June 2019. Revised August 2020. (23 pages) : Enseign. Math. 68 (2022) 1-24. Abstract.
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Large-scale rank and rigidity of the Weil-Petersson metric
Brian H. Bowditch
First draft: March 2015. Revised: January 2020. (43 pages) : Groups, Geom. Dyn. 14 (2020) 607-652. Abstract.
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Median and injective metric spaces
Brian H. Bowditch
First draft, November 2015. Revised, March 2016. (16 pages) : Math. Proc. Camb. Phil. Soc. 168 (2020) 43-55. Abstract.
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Notes on coarse median spaces
Brian H. Bowditch
First draft: March 2017. Revised: September 2017. (18 pages)
In ``Beyond hyperbolicity'', LMS Lecture Note Series, Vol. 454 (ed. M.Hagen, R.C.H.Webb, H.Wilton), Cambridge University Press (2019) 3-24. Abstract.
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The action of the mapping class group on the space of geodesic rays of a punctured hyperbolic surface
Brian H. Bowditch, Makoto Sakuma
August 2016. (13 pages) : Groups, Geom. Dyn. 12 (2018) 703-719. Abstract.
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Projections of the sphere graph to the arc graph of a surface
Brian H. Bowditch, Francesca Iezzi
First Draft, December 2015, Revised, July 2016. (18 pages) : J. Topol. Anal. 10 (2018) 245-261. Abstract.
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Large-scale rigidity properties of the mapping class groups
Brian H. Bowditch
First draft: March 2015. Revised: January 2017. (70 pages) : Pacific J. Math. 293 (2018) 1-73. Abstract.
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One-ended subgroups of mapping class groups
Brian H. Bowditch
First draft: October 2007. Revised: January 2015 (24 pages).
: in ``Hyperbolic geometry and geometric group theory'' (eds. K.Fujiwara, S.Kojima, K.Ohshika) Advanced Studies in Pure Mathematics, Mathematical Society of Japan (2017) 13-36. Abstract.
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Large-scale rank and rigidity of the Teichmüller metric
Brian H. Bowditch
First draft: March 2015. Revised: March 2016. (46 pages) : J. Topol. 9 (2016) 985-1020. Abstract.
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Rigidity of the strongly separating curve graph
Brian H. Bowditch
First draft: June 2014. Revised: April 2016. (23 pages) : Michigan Math. J. 65 (2016) 813-832. Abstract.
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Quasi-isometric maps between direct products of hyperbolic spaces
Brian H. Bowditch
First draft, April 2014. Revised, March 2016. (17 pages) : Internat. J. Algebra and Computation 26 (2016) 619-633. Abstract.
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Some properties of median metric spaces
Brian H. Bowditch
First Draft, July 2013, revised January 2015. (26 pages) : Groups, Geom. Dyn. 10 (2016) 279-317. Abstract.
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Quasiconvexity of bands in hyperbolic 3-manifolds
Brian H. Bowditch
First draft: November 2011. Revised: September 2013 (23 pages) : J. Austral. Math. Soc. 96 (2014) 167-185. Abstract.
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Uniform hyperbolicity of the curve graphs
Brian H. Bowditch
First draft: 11th December 2012. Revised: 24th June 2013. (12 pages) : Pacific J. Math. 269 (2014) 269-280. Abstract.
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Embedding median algebras in products of trees
Brian H. Bowditch
First draft, November 2011. Revised, May 2013. (27 pages) : Geom. Dedicata 170 (2014) 157-176. Abstract.
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Stacks of hyperbolic spaces and ends of 3-manifolds
Brian H. Bowditch
February 2002, revised February 2011 (96 pages).
in ``Geometry and Topology Down Under'', Contemporary Mathematics Vol. 597, (eds. C.D.Hodgson, W.H.Jaco, M.G.Scharlemann, S.Tillman) American Mathematical Society (2013) 65-138. (96 pages) Abstract.
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Coarse median spaces and groups
Brian H. Bowditch
November 2011. (42 pages) : Pacific J. Math. 261 (2013) 53-93. Abstract.
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Invariance of coarse median algebras under relative hyperbolicity
Brian H. Bowditch
December 2011. (15 pages) : Math. Proc. Camb. Phil. Soc. 154 (2013) 85-95. Abstract.
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An upper bound for injectivity radii in convex cores
Brian H. Bowditch
First draft: May 2010. Revised, July 2011. (16 pages) : Groups, Geom. Dyn. 7 (2013) 109-126. Abstract.
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Relatively hyperbolic groups
B.H. Bowditch
First draft: July 1997. Revised: September 2011. (75 pages) : Internat. J. Algebra and Computation. 22 (2012) 1250016, 66pp. Abstract.
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Notes on tameness
Brian H. Bowditch
First draft: June 2006. Revised: November 2009. (45 pages) : Enseign. Math. 56 (2010) 229-285. Abstract.
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Atoroidal surface bundles over surfaces
Brian H. Bowditch
First draft: June 2007. Revised: October 2009 (46 pages) : Geom. Funct. Anal. 19 (2009) 943-988. Abstract.
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Tight geodesics in the curve complex
Brian H. Bowditch
First draft: October 2003. Revised: November 2003. (16 pages) : Invent. Math. 171 (2008) 281-300. Abstract.
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Length bounds on curves arising from tight geodesics
Brian H. Bowditch
First draft: November 2003. Revised: March 2007. (33 pages) : Geom. Funct. Anal. 17 (2007) 1001-1042. Abstract.
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Systems of bands in hyperbolic 3-manifolds
Brian H. Bowditch
First draft: October 2003. Revised: February 2007 : Pacific J. Math. 232 (2007) 1-42. Abstract.
Text (36 pages). [Download dvi] [Download pdf (284K)]
Figures. First page: [Download pdf (12K)]. Second page: [Download pdf (29K)]

The angel game in the plane
Brian H. Bowditch
First draft: August 2006. Revised: September 2006. (18 pages) : Combin. Probab. Comput. 16 (2007) 345-362. Abstract.
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The Cannon-Thurston map for punctured-surface groups
Brian H. Bowditch
First draft: December 2001. Revised: February 2002. (48 pages) : Math. Z. 255 (2007) 35-76. Abstract.
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A course on geometric group theory
Brian H. Bowditch
October 2005. : MSJ Mem. Vol 16 (2006) Abstract.
[Download dvi] (65 pages: No pictures!)
[Download pdf (459K)] (72 pages: With pictures.)

Intersection numbers and the hyperbolicity of the curve complex
Brian H. Bowditch
First draft: July 2002. Revised: September 2002 (23 pages) : J. reine angew. Math. 598 (2006) 105-129. Abstract.
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Hyperbolic 3-manifolds and the geometry of the curve complex
Brian H. Bowditch
September 2004. (13 pages) : in ``European Congress of Mathematics, Stockholm, June 27 - July 2, 2004'' (ed. A.Laptev) European Mathematical Society Publishing House (2005) 103-115. Abstract.
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Hausdorff dimension and dendritic limit sets
Brian H. Bowditch
January 2003. (8 pages) : Math. Annalen 332 (2005) 667-676. Abstract.
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Planar groups and the Seifert conjecture
B.H. Bowditch
First draft: December 1998. Revised: November 1999. (51 pages) : J. reine angew. Math. 576 (2004) 11-62. Abstract.
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Groups acting on Cantor sets and the end structure of graphs
B.H. Bowditch
First draft: February 2000. Revised: January 2001. (26 pages) : Pacific J. Math. 207 (2002) 31-60. Abstract.
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Splittings of finitely generated groups over two-ended subgroups
B.H. Bowditch
First draft: November 1999. Revised: January 2001. (34 pages) : Trans. Amer. Math. Soc. 354 (2002) 1049-1078. Abstract.
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Peripheral splittings of groups
B.H. Bowditch
First draft: January 1998. Revised: January 2001. (28 pages) : Trans. Amer. Math. Soc. 353 (2001) 4057-4082. Abstract.
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Archimedean actions on median pretrees
B.H. Bowditch, J. Crisp
Math. Proc. Camb. Phil. Soc. 130 (2001) 383-400. (17 pages) Abstract.
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A variation on the unique product property
Brian H. Bowditch
J. London Math. Soc. 62 (2000) 813-826. (15 pages) Abstract.
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Boundaries of geometrically finite groups
B.H. Bowditch
Math. Z. 230 (1999) 509-527. (16 pages, no pictures) Abstract.
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Connectedness properties of limit sets
B.H. Bowditch
Trans. Amer. Math. Soc. 351 (1999) 3673-3686. (14 pages) Abstract.
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Treelike structures arising from continua and convergence groups
B.H. Bowditch
Memoirs Amer. Math. Soc. 662 (1999). (85 pages) Abstract.
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Convergence groups and configuration spaces
B.H. Bowditch
in ``Geometric Group Theory Down Under, proceedings of a Special Year in Geometric Group Theory, Canberra, Australia'' (ed. J.Cossey, C.F.Miller III, W.D.Neumann, M.Shapiro), de Gruyter (1999), 23-54. (31 pages) Abstract.
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Boundaries of strongly accessible hyperbolic groups
B.H. Bowditch,
revised November 1997
in ``The Epstein Birthday Schrift'', Geometry and Topology Monographs Volume 1, (ed. I.Rivin, C.Rourke, C.Series) International Press (1998) 51-97. (39 pages) Abstract.
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A topological characterisation of hyperbolic groups
B.H. Bowditch
J. Amer. Math. Soc. 11 (1998) 643-667. (28 pages) Abstract.
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Group actions on trees and dendrons
B.H. Bowditch
Topology 37 (1998) 1275-1298. (26 pages) Abstract.
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Cut points and canonical splittings of hyperbolic groups
B.H. Bowditch
Acta Math. 180 (1998) 145-186. (38 pages) Abstract.
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Continuously many quasiisometry classes of 2-generator groups
B.H. Bowditch
Comment. Math. Helv. 73 (1998) 232-236. (5 pages) Abstract.
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Spaces of geometrically finite representations
B.H. Bowditch
Ann. Acad. Sci. Fenn. Math. 23 (1998) 389-414. (24 pages) Abstract.
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Markoff triples and quasifuchsian groups
B.H. Bowditch
Proc. Lond. Math. Soc. 77 (1998) 697-736. (42 pages) Abstract.
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A variation of McShane's identity for once-punctured torus bundles
B.H. Bowditch
Topology 36 (1997) 325-334. (10 pages, without pictures) Abstract.
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A class of incomplete non-positively curved manifolds
B.H. Bowditch
Pacific J. Math. 172 (1996) 1-39. (33 pages) Abstract.
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A proof of McShane's identity via Markoff triples
B.H. Bowditch
Bull. London Math. Soc. 28 (1996) 73-78. (6 pages) Abstract.
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Minkowskian subspaces of non-positively curved metric spaces
B.H. Bowditch
Bull. London Math. Soc. 27 (1995) 575-584. (11 pages, without pictures) Abstract.
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A short proof that a subquadratic isoperimetric inequality implies a linear one
B.H. Bowditch
Michigan Math. J. 42 (1995) 103-107. (4 pages, without pictures) Abstract.
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Geometrical finiteness with variable negative curvature
B.H. Bowditch
Duke Math. J., 77 (1995) 229-274. (44 pages, without pictures) Abstract.
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A 4-dimensional Kleinian group
B.H. Bowditch, G.Mess
Trans. Amer. Math. Soc. 344 (1994) 391-405. (13 pages, without pictures) Abstract.
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Some results on the geometry of convex hulls in manifolds of pinched negative curvature
B.H. Bowditch
Comment. Math. Helv. 69 (1994) 49-81. (25 pages, without pictures) Abstract.
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Discrete parabolic groups
B.H. Bowditch
J. Differential Geom. 38 (1993) 559-583. (21 pages, without pictures) Abstract.
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The minimal volume of the plane
B.H. Bowditch
J. Austral. Math. Soc. 55 (1993) 23-40. (14 pages, without pictures) Abstract.
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Geometrical finiteness for hyperbolic groups
B.H. Bowditch
J. Funct. Anal. 113 (1993) 245-317. (56 pages, without pictures) Abstract.
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Singular euclidean structures on surfaces
B.H. Bowditch
J. London Math. Soc. 44 (1991) 553-565. (11 pages, without pictures) Abstract.
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Scanned preprints:

The following is a preprint version of a published article, now apparently out of print.

Notes on Gromov's hyperbolicity criterion for path-metric spaces
B.H. Bowditch
IHES preprint version, June 1990.
Published version in: ``Group theory from a geometrical viewpoint'' (ed. E.Ghys, A.H aefliger, A.Verjovsky) World Scientific (1991) 64-167. Abstract.
Chapters 0-6. (58 pages)[Scanned pdf (1462K)]
Chapters 7-8. (40 pages)[Scanned pdf (1215K)]

The following is a preprint version of another published article.

Notes on locally CAT(1) spaces
B.H. Bowditch
Aberdeen preprint version, 1992.
Published version in ``Geometric group theory'', (ed. R. Charney, M. Davis, M. Shapiro), de Gruyter (1995) 1-48. Abstract.
Chapters 0-6. (58 pages)[Scanned pdf (1460K)]


Redundant papers:

The following two papers are superseded by ``The ending lamination theorem'' paper, posted above.

End invariants of hyperbolic 3-manifolds
Brian H. Bowditch
December 2005 (32 pages). Abstract.
[Download dvi] [Download pdf (252K)]

Geometric models for hyperbolic 3-manifolds
Brian H. Bowditch
First draft: August 2005. Revised: October 2006 (81 pages). Abstract.
[Download dvi] [Download pdf (544K)]

The following paper is superseded by `Large-scale rigidity properties of the mapping class groups'' and ``Large-scale rank and rigidity of the Weil-Petersson metric'' posted above.

Rank and rigidity properties of spaces associated to a surface
Brian H. Bowditch
First draft, April 2014. Revised, October 2014. Abstract.
[Download pdf]

The following paper is superseded by: ``Large-scale rank and rigidity of the Teichmüller metric'' posted above.

The coarse geometry of the Teichmüller metric
Brian H. Bowditch
First draft, October 2014. Revised, March 2015. Abstract.
[Download pdf]


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