4–fold symmetric quandle invariants of 3–manifolds

Nosaka, Takefumi¹

¹Research Institute for Mathematical Sciences, Kyoto University, Sakyo-ku, Kyoto 606-8502, Japan

Algebraic and Geometric Topology, Tome 11 (2011) no. 3, pp. 1601-1648

Résumé

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.

Détail

DOI : 10.2140/agt.2011.11.1601

Classification : 57M12, 57M25, 57M27, 57N70, 58K65, 55Q52, 22A30, 11E57, 55R40, 05E15
Keywords: quandle, symmetric quandle, quandle cocycle invariant, the rack space, link, $3$–manifold, branched covering

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