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2011 $4$–fold symmetric quandle invariants of $3$–manifolds
Takefumi Nosaka
Algebr. Geom. Topol. 11(3): 1601-1648 (2011). DOI: 10.2140/agt.2011.11.1601

Abstract

The paper introduces 4–fold symmetric quandles and 4–fold symmetric quandle homotopy invariants of 3–manifolds. We classify 4–fold symmetric quandles and investigate their properties. When the quandle is finite, we explicitly determine a presentation of its inner automorphism group. We calculate the container of the 4–fold symmetric quandle homotopy invariant. We also discuss symmetric quandle cocycle invariants and coloring polynomials of 4–fold symmetric quandles.

Citation

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Takefumi Nosaka. "$4$–fold symmetric quandle invariants of $3$–manifolds." Algebr. Geom. Topol. 11 (3) 1601 - 1648, 2011. https://doi.org/10.2140/agt.2011.11.1601

Information

Received: 4 November 2010; Revised: 22 March 2011; Accepted: 24 March 2011; Published: 2011
First available in Project Euclid: 19 December 2017

zbMATH: 1230.57015
MathSciNet: MR2821435
Digital Object Identifier: 10.2140/agt.2011.11.1601

Subjects:
Primary: 57M12, 57M25, 57M27, 57N70, 58K65
Secondary: 05E15, 11E57, 22A30, 55Q52, 55R40

Rights: Copyright © 2011 Mathematical Sciences Publishers

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