2004/11/02 by Nicholas Jackson, Jackson, Nicholas
Mathematics · #Algebraic structures and combinatorial models #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #math.CT #math.GT #msc:18E10 #msc:18G35 #msc:18G60
paper · pdf · doi:10.48550/arxiv.math/0411055
16 pages, LaTeX2e. Requires gtart.cls and diagram.sty (included)
arxiv created 2004/11/02 · arxiv updated 2009/12/01
The theory of rack and quandle modules is developed - in particular a tensor product is defined, and shown to satisfy an appropriate adjointness condition. Notions of free rack and quandle modules are introduced, and used to define an enveloping object (the `rack algebra' or `wring') for a given rack or quandle. These constructions are then used to define homology and cohomology theories for racks and quandles which contain all currently-known variants.