SKEIN ALGEBRAS OF SURFACES

被引：21

作者：

Przytycki, Jozef H. ^{[1
,2
]}

Sikora, Adam S. ^{[3
]}

机构：

[1] George Washington Univ, Dept Math, Washington, DC 20052 USA

[2] Univ Gdansk, Dept Math Phys & Informat, Wita Stwosza 57, PL-80952 Gdansk, Poland

[3] SUNY Buffalo, Dept Math, Buffalo, NY 14260 USA

来源：

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY | 2019年 / 371卷 / 02期

基金：

美国国家科学基金会;

关键词：

Kauffman bracket skein module; skein algebra; Dehn-Thurston numbers; REPRESENTATION VARIETIES; CHARACTER VARIETIES; FUNDAMENTAL-GROUPS; KAUFFMAN; MODULES; ROOTS;

D O I：

10.1090/tran/7298

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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.

引用

页码：1309 / 1332

页数：24

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