Kauffman state sums and bracket deformation

Nikos Apostolakis; Uwe Kaiser

doi:10.1142/S0218216507005567

Kauffman state sums and bracket deformation

Nikos Apostolakis, Uwe Kaiser

Mathematics Department

BCC of CUNY

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

Abstract

We derive a formula expanding the bracket with respect to a natural deformation parameter. The expansion is in terms of a two-variable polynomial algebra of diagram resolutions generated by basic operations involving the Goldman bracket. A functorial characterization of this algebra is given. Differentiability properties of the star product underlying the Kauffman bracket are discussed.

Original language	English
Pages (from-to)	809-831
Number of pages	23
Journal	Journal of Knot Theory and its Ramifications
Volume	16
Issue number	7
DOIs	https://doi.org/10.1142/S0218216507005567
State	Published - Sep 2007

Keywords

Deformation quantization
Goldman bracket
Kauffman bracket
Mapping class group
State sum
String topology

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abstract = "We derive a formula expanding the bracket with respect to a natural deformation parameter. The expansion is in terms of a two-variable polynomial algebra of diagram resolutions generated by basic operations involving the Goldman bracket. A functorial characterization of this algebra is given. Differentiability properties of the star product underlying the Kauffman bracket are discussed.",

keywords = "Deformation quantization, Goldman bracket, Kauffman bracket, Mapping class group, State sum, String topology",

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T1 - Kauffman state sums and bracket deformation

AU - Apostolakis, Nikos

AU - Kaiser, Uwe

PY - 2007/9

Y1 - 2007/9

N2 - We derive a formula expanding the bracket with respect to a natural deformation parameter. The expansion is in terms of a two-variable polynomial algebra of diagram resolutions generated by basic operations involving the Goldman bracket. A functorial characterization of this algebra is given. Differentiability properties of the star product underlying the Kauffman bracket are discussed.

AB - We derive a formula expanding the bracket with respect to a natural deformation parameter. The expansion is in terms of a two-variable polynomial algebra of diagram resolutions generated by basic operations involving the Goldman bracket. A functorial characterization of this algebra is given. Differentiability properties of the star product underlying the Kauffman bracket are discussed.

KW - Deformation quantization

KW - Goldman bracket

KW - Kauffman bracket

KW - Mapping class group

KW - State sum

KW - String topology

UR - https://www.scopus.com/pages/publications/34548312121

U2 - 10.1142/S0218216507005567

DO - 10.1142/S0218216507005567

M3 - Article

AN - SCOPUS:34548312121

SN - 0218-2165

VL - 16

SP - 809

EP - 831

JO - Journal of Knot Theory and its Ramifications

JF - Journal of Knot Theory and its Ramifications

IS - 7

ER -

Kauffman state sums and bracket deformation

Abstract

Keywords

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