Quandle homotopy invariants of knotted surfaces

Takefumi Nosaka

研究成果: ジャーナルへの寄稿学術誌査読

8 被引用数 (Scopus)

抄録

Given a finite quandle, we introduce a quandle homotopy invariant of knotted surfaces in the 4-sphere, modifying that of classical links. This invariant is valued in the third homotopy group of the quandle space, and is universal among the (generalized) quandle cocycle invariants. We compute the second and third homotopy groups, with respect to "regular Alexander quandles". As a corollary, any quandle cocycle invariant using the dihedral quandle of prime order is a scalar multiple of Mochizuki 3-cocycle invariant. As another result, we determine the third quandle homology group of the dihedral quandle of odd order.

本文言語英語
ページ(範囲)341-365
ページ数25
ジャーナルMathematische Zeitschrift
274
1-2
DOI
出版ステータス出版済み - 6月 2013

!!!All Science Journal Classification (ASJC) codes

  • 数学 (全般)

フィンガープリント

「Quandle homotopy invariants of knotted surfaces」の研究トピックを掘り下げます。これらがまとまってユニークなフィンガープリントを構成します。

引用スタイル