4–fold symmetric quandle invariants of 3–manifolds

Nosaka, Takefumi

doi:10.2140/agt.2011.11.1601

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$4$–fold symmetric quandle invariants of $3$–manifolds

Takefumi Nosaka

Algebraic & Geometric Topology 11 (2011) 1601–1648

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.

Keywords

quandle, symmetric quandle, quandle cocycle invariant, the rack space, link, $3$–manifold, branched covering

Mathematical Subject Classification 2010

Primary: 57M12, 57M25, 57M27, 57N70, 58K65

Secondary: 55Q52, 22A30, 11E57, 55R40, 05E15

References

Publication

Received: 4 November 2010

Revised: 22 March 2011

Accepted: 24 March 2011

Published: 3 June 2011

Authors

Takefumi Nosaka
Research Institute for Mathematical Sciences Kyoto University Sakyo-ku Kyoto 606-8502 Japan

Volume 11, issue 3 (2011)