Skein algebras of surfaces

Józef Henryk Przytycki , Adam S. Sikora

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.
Author Józef Henryk Przytycki (FMPI / IM)
Józef Henryk Przytycki,,
- Institute of Mathematics
, Adam S. Sikora
Adam S. Sikora,,
-
Journal seriesTransactions of the American Mathematical Society, ISSN 0002-9947, (A 40 pkt)
Issue year2019
Vol371
No2
Pages1309-1332
Publication size in sheets1.15
Keywords in EnglishKauffman bracket skein module, skein algebra, Dehn-Thurston numbers
DOIDOI:10.1090/tran/7298
Languageen angielski
Score (nominal)40
ScoreMinisterial score = 40.0, 13-11-2018, ArticleFromJournal
Ministerial score (2013-2016) = 40.0, 13-11-2018, ArticleFromJournal
Publication indicators WoS Impact Factor: 2016 = 1.426 (2) - 2016=1.362 (5)
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