Quandles and Topological Pairs by Takefumi Nosaka

Author:Takefumi Nosaka
Language: eng
Format: epub
Publisher: Springer Singapore, Singapore

(6.9)

Here is a group ring of A. Inspired by this (6.9), when X is a connected quandle, we define a certain (-equivariant) part of the Dijkgraaf-Witten invariant of branched covering spaces as a map

(6.10)

Using this, we readily obtain from Theorem 6.19 and Corollary 6.4 that

Corollary 6.20

[N7]] Let X and be as above, and let be a prime which is coprime to . Take the Hurewicz map as in (6.4), and denote by the right side in (5.​5). Assume that and that is finitely generated.

Then, for any X-coloring of any link L, the -torsion of the quandle homotopy invariant of is decomposed as

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