R. A. Litherland, Sam Nelson
Published 2001-06-19, updated 2001-10-26Version 4
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.
Comments: LaTeX, 16 pages; v3.0 added author contact info & corrected typos
Journal: J. Pure Appl. Algebra 178 (2003) 187-202
Varieties of general type with the same Betti numbers as $\mathbb P^1\times \mathbb P^1\times\ldots\times \mathbb P^1$
Sutured manifolds and $L^2$-Betti numbers
Irrational pencils and Betti numbers
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