The Betti numbers of some finite racks

2001/06/30 by R. A. Litherland, Sam Nelson · 1 citation
Mathematics · #math.GT #math.AT #msc:55M27 #msc:55N35

paper · pdf

published as J. Pure Appl. Algebra 178 (2003) 187-202 · LaTeX, 16 pages; v3.0 added author contact info & corrected typos

arxiv created 2001/10/26 · arxiv updated 2009/11/30

Abstract

We show that the lower bounds for Betti numbers given in math.GT/9909161 are equalities for a class of racks that includes dihedral and Alexander racks. We confirm a conjecture from the same paper by defining a splitting for the short exact sequence of quandle chain complexes. We define isomorphisms between Alexander racks of certain forms, and we also list the second and third homology groups of some dihedral and Alexander quandles.

Cited by

• Structure groups and second homology groups of linear Alexander quandles

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