Volume 11, issue 3 (2011)

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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
$4$–fold symmetric quandle invariants of $3$–manifolds

Takefumi Nosaka

Algebraic & Geometric Topology 11 (2011) 1601–1648
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