4-fold symmetric quandle invariants of 3-manifolds

Takefumi Nosaka

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)1601-1648
Number of pages48
JournalAlgebraic and Geometric Topology
Issue number3
Publication statusPublished - 2011
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Geometry and Topology


Dive into the research topics of '4-fold symmetric quandle invariants of 3-manifolds'. Together they form a unique fingerprint.

Cite this