4-fold symmetric quandle invariants of 3-manifolds

Takefumi Nosaka

Research output: Contribution to journalArticle

2 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)1601-1648
Number of pages48
JournalAlgebraic and Geometric Topology
Volume11
Issue number3
DOIs
Publication statusPublished - Aug 2 2011

Fingerprint

Quandle
Fold
Invariant
Homotopy
Cocycle
Container
Automorphism Group
Colouring
Classify
Calculate
Polynomial

All Science Journal Classification (ASJC) codes

  • Geometry and Topology

Cite this

4-fold symmetric quandle invariants of 3-manifolds. / Nosaka, Takefumi.

In: Algebraic and Geometric Topology, Vol. 11, No. 3, 02.08.2011, p. 1601-1648.

Research output: Contribution to journalArticle

Nosaka, Takefumi. / 4-fold symmetric quandle invariants of 3-manifolds. In: Algebraic and Geometric Topology. 2011 ; Vol. 11, No. 3. pp. 1601-1648.
@article{791daf55c1ec4295bf16b15be7e39b5d,
title = "4-fold symmetric quandle invariants of 3-manifolds",
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.",
author = "Takefumi Nosaka",
year = "2011",
month = "8",
day = "2",
doi = "10.2140/agt.2011.11.1601",
language = "English",
volume = "11",
pages = "1601--1648",
journal = "Algebraic and Geometric Topology",
issn = "1472-2747",
publisher = "Agriculture.gr",
number = "3",

}

TY - JOUR

T1 - 4-fold symmetric quandle invariants of 3-manifolds

AU - Nosaka, Takefumi

PY - 2011/8/2

Y1 - 2011/8/2

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=79960876710&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=79960876710&partnerID=8YFLogxK

U2 - 10.2140/agt.2011.11.1601

DO - 10.2140/agt.2011.11.1601

M3 - Article

VL - 11

SP - 1601

EP - 1648

JO - Algebraic and Geometric Topology

JF - Algebraic and Geometric Topology

SN - 1472-2747

IS - 3

ER -