Related papers: Truncated affine Rozansky--Witten models as extend…
We give a complete solution for the reduced Gromov-Witten theory of resolved surface singularities of type A_n, for any genus, with arbitrary descendent insertions. We also present a partial evaluation of the T-equivariant relative…
We proved a truncated second main theorem of level one with explicit exceptional sets for analytic maps into $\mathbb P^2$ intersecting the coordinate lines with sufficiently high multiplicities. As applications, we studied some cases of…
We extend the TFT construction of CFT correlators of [arXiv:hep-th/0204148] to so-called finite logarithmic CFTs for which the algebraic input data is no longer semisimple but still finite. More specifically, starting from the data of a…
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 4D TQFT. In this work, we compute the…
We establish a relation between fully extended $2$-dimensional TQFTs and recognisable weighted formal languages, rational biprefix codes and lattice TFTs. We show the equivalence of $2D$ closed TFTs and rational exchangeable series and we…
The aim of this note is to derive some invariants at infinity for open 3-manifolds in the framework of Topological Quantum Field Theories. These invariants may be used to test if an open manifold is simply connected at infinity as we done…
The algebraic structure of representation theory naturally arises from 2D fixed-point tensor network states, which conceptually formulates the pattern of long-range entanglement realized in such states. In 3D, the same underlying structure…
We extend the results of Deligne and Illusie on liftings modulo $p^2$ and decompositions of the de Rham complex in several ways. We show that for a smooth scheme $X$ over a perfect field $k$ of characteristic $p>0$, the truncations of the…
We give an alternative presentation of Khovanov homology of links with strict functoriality result over integers. The construction uses an oriented $sl(2)$ state model allowing a natural definition of the boundary operator as twisted action…
We prove that the restricted wreath product ${\mathbb{Z}_n \mathbin{\mathrm{wr}} \mathbb{Z}^k}$ has the $R_\infty$-property, i. e. every its automorphism $\varphi$ has infinite Reidemeister number $R(\varphi)$, in exactly two cases: (1) for…
A generalized-homology bordism-theory is constructed, such that for certain manifold homotopy stratified sets (MHSS; Quinn-spaces) homeomorphism-invariant geometric fundamental-classes exist. The construction combines three ideas: Firstly,…
Among (conformal) quantum field theories, the rational conformal field theories are singled out by the fact that their correlators can be constructed from a modular tensor category C with a distinguished object, a symmetric special…
We consider deformations of quantum exterior algebras extended by finite groups. Among these deformations are a class of algebras which we call truncated quantum Drinfeld Hecke algebras in view of their relation to classical Drinfeld Hecke…
We generalize the twisted quantum double model of topological orders in two dimensions to the case with boundaries by systematically constructing the boundary Hamiltonians. Given the bulk Hamiltonian defined by a gauge group $G$ and a…
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…
We investigate invertible projective representations and their 2-categorical analogues using the language of TQFTs with defects. The main result is a freeness property for invertible projective representatios. While trivial in the…
We consider a central extension of the mapping class group of a surface with a collection of framed colored points. The Witten-Reshetikhin-Turaev TQFTs associated to SU(2) and SO(3) induce linear representations of this group. We show that…
We develop the general theory for the construction of Extended Topological Quantum Field Theories (ETQFTs) associated with the Costantino-Geer-Patureau quantum invariants of closed 3-manifolds. In order to do so, we introduce relative…
We study how the fusion 2-category symmetry of a fermionic (2+1)d QFT can be affected when one allows for stacking with TQFTs to be an equivalence relation for QFTs. Focusing on a simple kind of fermionic fusion 2-category described purely…
Recent work explores the candidate phases of the 4d adjoint quantum chromodynamics (QCD$_4$) with an SU(2) gauge group and two massless adjoint Weyl fermions. Both Cordova-Dumitrescu and Bi-Senthil propose possible low energy 4d topological…