The Yang-Mills measure in the Kauffman bracket skein module

Doug Bullock; Charles Frohman; Joanna Kania-Bartoszynska

doi:10.1007/s000140300000

The Yang-Mills measure in the Kauffman bracket skein module

Doug Bullock, Charles Frohman, Joanna Kania-Bartoszynska

College of Arts and Sciences

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

11 Scopus citations

Abstract

For each closed, orientable surface Σ_g, we construct a local, diffeomorphism invariant trace on the Kauffman bracket skein module K_t(Σ_g × I). The trace is defined when |t| is neither 0 nor 1, and at certain roots of unity. At t = -1, the trace is integration against the symplectic measure on the SU(2) character variety of the fundamental group of Σ_g.

Original language	English
Pages (from-to)	1-17
Number of pages	17
Journal	Commentarii Mathematici Helvetici
Volume	78
Issue number	1
DOIs	https://doi.org/10.1007/s000140300000
State	Published - 2003

Keywords

Kauffman bracket
Quantum invariant
Skein
Symplectic measure
Trace

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10.1007/s000140300000

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abstract = "For each closed, orientable surface Σg, we construct a local, diffeomorphism invariant trace on the Kauffman bracket skein module Kt(Σg × I). The trace is defined when |t| is neither 0 nor 1, and at certain roots of unity. At t = -1, the trace is integration against the symplectic measure on the SU(2) character variety of the fundamental group of Σg.",

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N2 - For each closed, orientable surface Σg, we construct a local, diffeomorphism invariant trace on the Kauffman bracket skein module Kt(Σg × I). The trace is defined when |t| is neither 0 nor 1, and at certain roots of unity. At t = -1, the trace is integration against the symplectic measure on the SU(2) character variety of the fundamental group of Σg.

AB - For each closed, orientable surface Σg, we construct a local, diffeomorphism invariant trace on the Kauffman bracket skein module Kt(Σg × I). The trace is defined when |t| is neither 0 nor 1, and at certain roots of unity. At t = -1, the trace is integration against the symplectic measure on the SU(2) character variety of the fundamental group of Σg.

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KW - Quantum invariant

KW - Skein

KW - Symplectic measure

KW - Trace

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The Yang-Mills measure in the Kauffman bracket skein module

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Keywords

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