Topology Seminar
Tue, 19 April, 2016
9:00pm
Speaker: Adam S. Sikora (SUNY at Buffalo)
Title: Skein algebras of surfaces
Title: Skein algebras of surfaces
Abstract:
We show that the Kauffman bracket skein algebra of any oriented surface F has no zero-divisors and that its center is generated by knots parallel to the boundary of F.
Furthermore, we generalize the notion of skein algebras to skein algebras of marked surfaces and we prove analogous results them.
Our proofs rely on certain filtrations of skein algebras induced by pants decompositions of surfaces and by the associated Dehn-Thurston intersection numbers.
We show that the Kauffman bracket skein algebra of any oriented surface F has no zero-divisors and that its center is generated by knots parallel to the boundary of F.
Furthermore, we generalize the notion of skein algebras to skein algebras of marked surfaces and we prove analogous results them.
Our proofs rely on certain filtrations of skein algebras induced by pants decompositions of surfaces and by the associated Dehn-Thurston intersection numbers.
It is a joint work with Jozef Przytycki