The Betti numbers of some finite racks

Details The Betti numbers of some finite racks The Betti numbers of some finite racks

Publishing date

2001-06-19

URL

arxiv.org/abs/math/0106165v4

Journals

J. Pure Appl. Algebra 178 (2003) 187-202

Science

Mathematics

Field

Geometric Topology

Additional info

LaTeX, 16 pages; v3.0 added author contact info & corrected typos

Type

Scientific paper

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.

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