Non-Semisimple Topological Quantum Field Theories for 3-Manifolds with Corners
By T. Kerler, V. Lyubashenko. 2001
203 citations recorded by the source corpus.
Subfields: Computational Theory and Mathematics, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/367dceca3145303968fd8d85d877b9fca94283bb
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Computational Theory and Mathematics
- Kenichi Shimizu
- Christopher J. Schommer-Pries
- Kazuo Habiro
- O. Y. Viro
- L. Rozansky
- I. Tipunin
- A. M. Semikhatov
- B. Feigin
In Geometry and Topology
- Stavros Garoufalidis
- Kenichi Shimizu
- Jacob Rasmussen
- Kazuo Habiro
- G. Massuyeau
- L. Rozansky
- Tomotada Ohtsuki
- A. Gainutdinov
In Mathematical Physics
- Kenichi Shimizu
- Stavros Garoufalidis
- Jacob Rasmussen
- Kazuo Habiro
- L. Rozansky
- G. Massuyeau
- Tomotada Ohtsuki
- Dror Bar-Natan
Citations in the corpus
- Non-degeneracy conditions for braided finite tensor categories (2016, methodology): “As explained in [KL01], a ‘non-semisimple’ modular tensor category in this sense also yields an invariant of closed 3-manifolds and a projective representation of the mapping class group of a closed surface as in the semisimple case.”
- Nonsemisimple Fusion Algebras and the Verlinde Formula (2003, background): “(For one proposal on how to associate a three-dimensional TFT to a nonrational CFT, see [29].”
- Problems on invariants of knots and 3-manifolds (2004, background): “Already in [216] it is clear that there are several choices.”
- The Classification of Two-Dimensional Extended Topological Field Theories (2011, background): “Previous attempts at defining the bordism bicategory have been made in [KL01] and [Mor07], but neither of these is quite adequate.”
- Bottom tangles and universal invariants (2005, background): “(See also Habiro [22], Kerler [39; 42], Kerler–Lyubashenko [43] and Yetter [85] for descriptions of C .”
- Logarithmic extensions of minimal models: characters and modular transformations. (2006, background): “3.1, which are evidentlyWp+,p−-modules because of their description in (3.20).”
- Hopf monads (2006, background): “A more general setting for constructing quantum invariants of 3-manifolds has been subsequently developed in [8], and more recently in [7,16], where the input data is a (non-necessarily semisimple) ribbon category C which admits a coend A = ∫ X∈C ∨X ⊗ X.”