Skein algebras of surfaces

Józef H. Przytycki; Adam S. Sikora

doi:10.1090/tran/7298

Skein algebras of surfaces

Józef H. Przytycki
, Adam S. Sikora

Mathematics

George Washington University
University of Gdańsk

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

24 Scopus citations

Abstract

We show that the Kauffman bracket skein algebra of any oriented surface F (possibly with marked points in its boundary) has no zero divisors and that its center is generated by knots parallel to the unmarked components of the boundary of F . Furthermore, we show that skein algebras are Noetherian and Ore. Our proofs rely on certain filtrations of skein algebras induced by pants decompositions of surfaces. We prove some basic algebraic properties of the associated graded algebras along the way.

Original language	English
Pages (from-to)	1309-1332
Number of pages	24
Journal	Transactions of the American Mathematical Society
Volume	371
Issue number	2
DOIs	https://doi.org/10.1090/tran/7298
State	Published - Feb 1 2019

Keywords

Dehn-Thurston numbers
Kauffman bracket skein module
Skein algebra

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10.1090/tran/7298

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abstract = "We show that the Kauffman bracket skein algebra of any oriented surface F (possibly with marked points in its boundary) has no zero divisors and that its center is generated by knots parallel to the unmarked components of the boundary of F . Furthermore, we show that skein algebras are Noetherian and Ore. Our proofs rely on certain filtrations of skein algebras induced by pants decompositions of surfaces. We prove some basic algebraic properties of the associated graded algebras along the way.",

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KW - Dehn-Thurston numbers

KW - Kauffman bracket skein module

KW - Skein algebra

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Skein algebras of surfaces

Abstract

Keywords

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