Papers and preprints

Extensions of Racks and Quandles [ Postscript | PDF ]

Published: Homology, Homotopy and Applications 7:1 (2005) 151-167
arXiv: math.CT/0408040
A new notion of a `module' over a rack or a quandle is introduced, and it is shown that this construction includes all currently-known versions, and coincides with Beck's general definition of a module in an arbitrary category. These objects are then used to develop an Abelian extension theory for racks and quandles which generalises the second cohomology of the rack space, and also the quandle extension theories developed by Carter, Elhamdadi, Kamada and Saito.

Rack and quandle homology [ Postscript | PDF ]

arXiv: math.CT/0411055
Further development of the theory of rack and quandle modules, including the definition of free modules, the rack algebra (or wring), and a tensor product functor. These constructions are then used to define rack and quandle homology theories which contain all previously-known variants.