Deformation of String Topology into Homotopy Skein Modules

Uwe Kaiser

Deformation of String Topology into Homotopy Skein Modules

Mathematics Department

Research output: Contribution to journal › Article › peer-review

Abstract

Relations between the string topology of Chas and Sullivan and the homotopy skein modules of Hoste and Przytycki are studied. This provides new insight into the structure of homotopy skein modules and their meaning in the framework of quantum topology. Our results can be considered as weak extensions to all orientable 3–manifolds of classical results by Turaev and Goldman concerning intersection and skein theory on oriented surfaces.

Original language	American English
Journal	Algebraic & Geometric Topology
State	Published - 11 Oct 2003

Keywords

3-manifold
Lie algebra
deformation
free loop space
link homotopy
skein module
string topology
torsion

EGS Disciplines

Mathematics

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https://doi.org/10.2140/agt.2003.3.1005

Cite this

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title = "Deformation of String Topology into Homotopy Skein Modules",

abstract = " Relations between the string topology of Chas and Sullivan and the homotopy skein modules of Hoste and Przytycki are studied. This provides new insight into the structure of homotopy skein modules and their meaning in the framework of quantum topology. Our results can be considered as weak extensions to all orientable 3–manifolds of classical results by Turaev and Goldman concerning intersection and skein theory on oriented surfaces.",

keywords = "3-manifold, Lie algebra, deformation, free loop space, link homotopy, skein module, string topology, torsion",

author = "Uwe Kaiser",

year = "2003",

month = oct,

day = "11",

language = "American English",

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TY - JOUR

T1 - Deformation of String Topology into Homotopy Skein Modules

AU - Kaiser, Uwe

PY - 2003/10/11

Y1 - 2003/10/11

N2 - Relations between the string topology of Chas and Sullivan and the homotopy skein modules of Hoste and Przytycki are studied. This provides new insight into the structure of homotopy skein modules and their meaning in the framework of quantum topology. Our results can be considered as weak extensions to all orientable 3–manifolds of classical results by Turaev and Goldman concerning intersection and skein theory on oriented surfaces.

AB - Relations between the string topology of Chas and Sullivan and the homotopy skein modules of Hoste and Przytycki are studied. This provides new insight into the structure of homotopy skein modules and their meaning in the framework of quantum topology. Our results can be considered as weak extensions to all orientable 3–manifolds of classical results by Turaev and Goldman concerning intersection and skein theory on oriented surfaces.

KW - 3-manifold

KW - Lie algebra

KW - deformation

KW - free loop space

KW - link homotopy

KW - skein module

KW - string topology

KW - torsion

UR - https://scholarworks.boisestate.edu/math_facpubs/72

UR - https://doi.org/10.2140/agt.2003.3.1005

M3 - Article

JO - Algebraic & Geometric Topology

JF - Algebraic & Geometric Topology

ER -

Deformation of String Topology into Homotopy Skein Modules

Abstract

Keywords

EGS Disciplines

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