The Betti numbers of some finite racks
R. A. Litherland, Sam Nelson
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.
Create a lesson
Related papers
Chromatic Spherical and Renormalized Reshetikhin-Turaev Invariants for Drinfeld Centers
Nicolas Bridges, Shawn Cui, Nathan Geer
3-manifold decision problems and Riemann hypotheses
John A. Baldwin, Steven Sivek
On the (in)finiteness of fixed characters in genus 3
Yixuan Fu
Non-Pseudo-Arithmetic Hyperbolic 4-Manifolds
Alexander Kolpakov
Convex ribbon disks, quasipositivity, and Lagrangian sliceness
Joseph Breen, Alexander Zupan
A Smooth Shioda-Tate Isomorphism for Elliptically Fibered 4-Manifolds
Maria Morariu