Related papers: GL Verlinde numbers and the Grassmann TQFT
We construct a two-level weighted TQFT whose structure coefficents are equivariant intersection numbers on moduli spaces of admissible covers. Such a structure is parallel (and strictly related) to the local Gromov-Witten theory of curves…
We review our construction of the Teichm\"uller TQFT. We recall our volume conjecture for this TQFT and the examples for which this conjecture has been established. We end the paper with a brief review of our new formulation of the…
Motivated by Witten's work (arXiv:hep-th/9312104), we propose the Verlinde/Grassmannian correspondence which relates the GL Verlinde numbers to the K-theoretic quasimap invariants of the Grassmannian. We recover these two types of…
With the help of a new program, we do computations concerning the Witten-Reshetikhin-Turaev representations of mapping class groups. In particular we distinguish some mutant fibered knots. The program can be downloaded from…
We study (generalized) discrete symmetries of 2d semisimple TQFTs. These are 2d TQFTs whose fusion rules can be diagonalized. We show that, in this special basis, the 0-form symmetries always act as permutations while 1-form symmetries act…
An earlier paper gave a means of calculating the Lamb shift via Feynman diagrams. Here we apply the same techniques to TQFT.
The goal of the paper is an exposition of the simplest $(2+1)$-TQFTs in a sense following a pictorial approach. In the end, we fell short on details in the later sections where new results are stated and proofs are outlined. Comments are…
In this paper we propose a naive construction of 2-dimensional extended topological quantum field theories (TQFTs), which can be further generalized to the higher-dimension extended TQFTs.
We give an overview over several constructions of TQFT's over finite fields and cyclotomic integers and their applications to characterizing 3-manifolds and their fundamental groups.
We derive a canonical form for 2-group gauge theory in 3+1D which shows they are either equivalent to Dijkgraaf-Witten theory or to the so-called "EF1" topological order of Lan-Wen. According to that classification, recently argued from a…
We study Quot schemes of vector bundles on algebraic curves. Marian and Oprea gave a description of a topological quantum field theory (TQFT) studied by Witten in terms of intersection numbers on Quot schemes of trivial bundles. Since these…
In this paper, we show the equivalence between two seemingly distinct 2d TQFTs: one comes from the "Coulomb branch index" of the class S theory $T[\Sigma,G]$ on $L(k,1) \times S^1$, the other is the $^LG$ "equivariant Verlinde formula", or…
We endow a non-semisimple category of modules of unrolled quantum sl(2) with a Hermitian structure. We also prove that the TQFT constructed in arXiv:1202.3553 using this category is Hermitian. This gives rise to projective representations…
We provide a general construction of integral TQFTs over a general commutative ring, $\mathbf{k}$, starting from a finite Hopf algebra over $\mathbf{k}$ which is Frobenius and double balanced. These TQFTs specialize to the Hennings…
Gunningham [G] constructed an extended topological quantum field theory (TQFT) to obtain a closed formula for all spin Hurwitz numbers. In this note, we use the gluing theorem in [LP2] to re-prove the Gunningham's formula. We also describe…
For Grassmann varieties, we explain how the duality between the Gelfand-Tsetlin polytopes and the Feigin-Fourier-Littelmann-Vinberg polytopes arises from different positive structures.
By using quantum Teichm\"uller theory, we construct a one parameter family of TQFT's on the categroid of admissible leveled shaped 3-manifolds.
We study the cohomology of $G$-representation varieties and $G$-character stacks by means of a topological quantum field theory (TQFT). This TQFT is constructed as the composite of a so-called field theory and the 6-functor formalism of…
It is well-known that classical two-dimensional topological field theories are in one-to-one correspondence with commutative Frobenius algebras. An important extension of classical two-dimensional topological field theories is provided by…
In this article, we discuss a (2+1)-dimensional topological quantum field theory, for short TQFT, with a Verlinde basis. As a conclusion of this general theory, we have a Dehn surgery formula. We show that Turaev-Viro-Ocneanu TQFT has a…