Homotopical interpretation of link invariants from finite quandles

Takefumi Nosaka

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)

Abstract

This paper demonstrates a topological meaning of quandle cocycle invariants of links with respect to finite connected quandles X, from a perspective of homotopy theory: Specifically, for any prime ℓ which does not divide the type of X, the ℓ-torsion of this invariants is equal to a sum of the coloring polynomial and a Z-equivariant part of the Dijkgraaf-Witten invariant of a cyclic branched covering space. Moreover, our homotopical approach involves applications of computing some third homology groups and second homotopy groups of the classifying spaces of quandles, from results of group cohomology.

Original languageEnglish
Pages (from-to)1-30
Number of pages30
JournalTopology and its Applications
Volume193
DOIs
Publication statusPublished - Sep 5 2015

All Science Journal Classification (ASJC) codes

  • Geometry and Topology

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