Zobrazeno 1 - 10
of 248
pro vyhledávání: '"P. PATUREAU MIRAND"'
We study the density of the Burau representation from the perspective of a non-semisimple TQFT at a fourth root of unity. This gives a TQFT construction of Squier's Hermitian form on the Burau representation with possibly mixed signature. We prove th
Externí odkaz:
http://arxiv.org/abs/2402.13242
Using skein theory very much in the spirit of the Reshetikhin--Turaev constructions, we define a $(3+1)$-TQFT associated with possibly non-semisimple finite unimodular ribbon tensor categories. State spaces are given by admissible skein modules, and
Externí odkaz:
http://arxiv.org/abs/2306.03225
Chromatic maps for spherical tensor categories are instrumental tools to construct (non semisimple) invariants of 3-manifolds and their extension to (non compact) (2+1)-TQFTs. In this paper, we introduce left and right chromatic maps for finite tenso
Externí odkaz:
http://arxiv.org/abs/2305.14626
This paper contains three related groupings of results. First, we consider a new notion of an admissible skein module of a surface associated to an ideal in a (non-semisimple) pivotal category. Second, we introduce the notion of a chromatic category
Externí odkaz:
http://arxiv.org/abs/2302.04509
In this paper we introduce the notion of admissible skein modules associated to an ideal in a pivotal category. We explain how these modules are generalizations of the Kauffman skein algebra and how they relate to renormalized quantum invariants comi
Externí odkaz:
http://arxiv.org/abs/2302.04493
For $G$ a commutative group, we give a purely Hopf $G$-coalgebra construction of $G$-colored $3$-manifolds invariants using the notion of modified integral.
Comment: 18 pages
Comment: 18 pages
Externí odkaz:
http://arxiv.org/abs/2209.04691
Publikováno v:
Journal of the London Mathematical Society, Vol 109, Issue 1, 2024
We develop the categorical context for defining Hermitian non-semisimple TQFTs. We prove that relative Hermitian modular categories give rise to modified Hermitian WRT-TQFTs and provide numerous examples of these structures coming from the representa
Externí odkaz:
http://arxiv.org/abs/2208.14566
We study properties of relative modular categories and derive sufficient conditions for their existence. In particular, we derive sufficient conditions for relative pre-modular categories to be non-degenerate and relative modular, and for the quotien
Externí odkaz:
http://arxiv.org/abs/2110.15518
Publikováno v:
Annals of Physics, Volume 442, pg 168937, 2022
We construct large classes of exactly solvable pseudo-Hermitian 2D spin Hamiltonians. The ground states of these systems depend only on the spatial topology of the system. We identify the ground state system on a surface with the value assigned to th
Externí odkaz:
http://arxiv.org/abs/2108.10798
Publikováno v:
Letters in Mathematical Physics (2022), 112:74
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 of the mapp
Externí odkaz:
http://arxiv.org/abs/2108.09242