Volume 11, issue 3 (2011)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 19
Issue 3, 1079–1618
Issue 2, 533–1078
Issue 1, 1–532

Volume 18, 7 issues

Volume 17, 6 issues

Volume 16, 6 issues

Volume 15, 6 issues

Volume 14, 6 issues

Volume 13, 6 issues

Volume 12, 4 issues

Volume 11, 5 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 4 issues

Volume 7, 4 issues

Volume 6, 5 issues

Volume 5, 4 issues

Volume 4, 2 issues

Volume 3, 2 issues

Volume 2, 2 issues

Volume 1, 2 issues

The Journal
About the Journal
Subscriptions
Editorial Board
Editorial Interests
Editorial Procedure
Submission Guidelines
Submission Page
Ethics Statement
Author Index
To Appear
ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Other MSP Journals
$4$–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