Skein algebras of surfaces

By Józef H. Przytycki, Adam S. Sikora. Transactions of the American Mathematical Society, 2016

50 citations recorded by the source corpus.

We show that the Kauffman bracket skein algebra of any oriented surface F 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 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.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/8f4e8fcd5451a0b67f4b90cfecc63c36cd69660d

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In Geometry and Topology

1. J. Kania-Bartoszynska
2. Thang T. Q. Lê
3. C. Frohman
4. Adam S. Sikora
5. Józef H. Przytycki
6. Francesco Costantino
7. Helen M. Wong
8. Francis Bonahon

In Mathematical Physics

1. Thang T. Q. Lê
2. Adam S. Sikora
3. Józef H. Przytycki
4. Francesco Costantino
5. Helen M. Wong
6. Francis Bonahon

Citations in the corpus

• Unicity for representations of the Kauffman bracket skein algebra (2017, background): “ks (J s), where the k i range over all natural numbers, spans K (F). Another important property of K (F) is the following. 16 CHARLES FROHMAN, JOANNA KANIA-BARTOSZYNSKA, AND THANG LE^ Theorem 3.10 ([10, 36]). For any nite type surface F and any non-zero complex number , the skein algebra K (F) does ”
• Triangular decomposition of skein algebras (2016, background): “If ∂S is a closed manifold, then Ss(S) = S̊ (S), and the result is well-known and was proved in [PS2].”