## 19 Citations

### Relating quantum character varieties and skein modules

- Mathematics
- 2022

We relate the Kauffman bracket stated skein modules to two independent constructions of quantum representation spaces of Habiro and Van der Veen with the second author. We deduce from this relation a…

### Categorical Center of Higher Genera and 4D Factorization Homology

- Mathematics
- 2021

Many quantum invariants of knots and 3-manifolds (e.g. Jones polynomials) are special cases of the Witten-Reshetikhin-Turaev 3D TQFT. The latter is in turn a part of a larger theory the Crane-Yetter…

### Quantum decorated character stacks

- Mathematics
- 2021

We initiate the study of decorated character stacks and their quantizations using the framework of stratified factorization homology. We thereby extend the construction by Fock and Goncharov of…

### Kauffman skein algebras and quantum Teichmüller spaces via factorization homology

- MathematicsJournal of Knot Theory and Its Ramifications
- 2020

We compute the factorization homology of the four-punctured sphere and punctured torus over the quantum group [Formula: see text] explicitly as categories of equivariant modules using the framework…

### Stated skein modules of 3-manifolds and TQFT

- Mathematics
- 2022

. We study the behaviour of the Kauﬀman bracket skein modules of 3-manifolds under gluing along surfaces. For this purpose we extend the notion of Kauﬀman bracket skein modules to 3 -manifolds with…

### Finite presentations for stated skein algebras and lattice gauge field theory

- Mathematics
- 2020

We provide finite presentations for stated skein algebras and deduce that those algebras are Koszul and that they are isomorphic to the quantum moduli algebras appearing in lattice gauge field…

### Stated SL(n)-Skein Modules and Algebras

- Mathematics
- 2021

We develop a theory of stated SL(n)-skein modules, Sn(M,N ), of 3-manifolds M marked with intervals N in their boundaries. These skein modules, generalizing stated SL(2)-modules of the first author,…

### The $\mathfrak{gl}_2$-Skein Module of Lens Spaces via the Torus and Solid Torus

- Mathematics
- 2021

We compute the action of the gl2-skein algebra of the torus on the gl2-skein module of the solid torus. As a result, we show that the gl 2 -skein modules of lens spaces is spanned by (⌊

### Relating stated skein algebras and internal skein algebras

- Mathematics
- 2021

. We give an explicit correspondence between stated skein algebras, which are deﬁned via explicit relations on stated tangles in [Costantino F., Lˆe T.T.Q., arXiv:1907.11400], and internal skein…

### Factorization homology and 4D TQFT

- MathematicsQuantum Topology
- 2022

In [BK], it is shown that the Turaev-Viro invariants defined for a spherical fusion category $\mathcal{A}$ extends to invariants of 3-manifolds with corners. In [Kir], an equivalent formulation for…

## References

SHOWING 1-10 OF 29 REFERENCES

### Higher categories, colimits, and the blob complex

- MathematicsProceedings of the National Academy of Sciences
- 2011

The important properties of the blob complex are outlined and the proof of a generalization of Deligne’s conjecture on Hochschild cohomology and the little discs operad to higher dimensions is sketched.

### Integrating quantum groups over surfaces

- MathematicsJournal of Topology
- 2018

We apply the mechanism of factorization homology to construct and compute category‐valued two‐dimensional topological field theories associated to braided tensor categories, generalizing the…

### Kauffman skein algebras and quantum Teichmüller spaces via factorization homology

- MathematicsJournal of Knot Theory and Its Ramifications
- 2020

We compute the factorization homology of the four-punctured sphere and punctured torus over the quantum group [Formula: see text] explicitly as categories of equivariant modules using the framework…

### Quantum Invariants of Knots and 3-Manifolds

- Physics
- 1994

This monograph, now in its second revised edition, provides a systematic treatment of topological quantum field theories in three dimensions, inspired by the discovery of the Jones polynomial of…

### Ribbon graphs and their invaraints derived from quantum groups

- Mathematics
- 1990

The generalization of Jones polynomial of links to the case of graphs inR3 is presented. It is constructed as the functor from the category of graphs to the category of representations of the quantum…

### Skein theory for SU(n)-quantum invariants

- Mathematics
- 2005

For any n ≥ 2 we define an isotopy invariant, h i n , for a certain set of n-valent ribbon graphs in R 3 , including all framed oriented links. We show that our bracket coincides with the Kauffman…

### A Duality for Modules over Monoidal Categories of Representations of Semisimple Hopf Algebras

- Mathematics
- 2001

For a finite dimensional semisimple cosemisimple Hopf algebra A and its dual Hopf algebra B, we set up a natural one-to-one correspondence between categories with actions of the monoidal categories…

### Skein quantization of Poisson algebras of loops on surfaces

- Mathematics
- 1991

© Gauthier-Villars (Éditions scientifiques et médicales Elsevier), 1991, tous droits réservés. L’accès aux archives de la revue « Annales scientifiques de l’É.N.S. » (http://www.…