Resources and Papers

Here are some books I recommend if you're interested in reading more about skein modules, quantum groups, or character varieties.

Theory of Skein Modules

• Jozef Prztycki - Lectures in Knot Theory

• Vladimir Turaev - Quantum Invariants of Knots and 3-Manifolds

• Vladimir Turaev - "Skein quantization of Poisson algebra of loops on surfaces"

Quantum Groups

• Chrisitan Kassel - Quantum Groups

• Chari and Pressley - A Guide to Quantum Groups, for a more geometric approach.

Here are some papers going into more depth.

Historical Papers

• Witten - Quantum Field Theory and the Jones Polynomial

• Przytycki and Sikora - On Skein Algebras and Sl(2)-Character Varieties

Stated Skein Modules

• Bonahon and Wong -  Quantum Traces for Representations of Surface Groups in SL_2

• Costantino and Le - Stated Skein Algebras of Surfaces

Some Big Recent Results

Proof of Witten's Finiteness Conjecture in 2023

• Gunningham, Jordan, and Safranov - The Finiteness Conjecture for Skein Modules

• Belletti and Detcherry - An Effective Proof of Finiteness for Kauffman Bracket Skein Modules

An Algebraic Detection of Exotic 4-Manifolds in 2024 (Not using the Kauffman bracket, but still interesting.)

• Ren and Willis - Khovanov Homology and Exotic 4-Manifolds

Talks, Seminars, and Conferences to look out for

Quantum Topology, Character Varieties, and Low-Dimensional Topology

• Tutorials (September 24-29)

• Workshop I: Hyperbolic Structures and Quantum Invariants (October 12-15)

• Workshop II: Contact Geometry, Cluster Algebras and Skein Theory (October 26-29)

• Workshop III: Categorification in Quantum Topology (November 16-19)

Journees de Topologie Quantique (October 19)

New Trends in Low-Dimensional Topology (December 7-11)