164 citations · 251 across the 20 of their papers we have counts for
23 papers
Quantum invariants of flat 2-bundles over 3-manifolds
Kursat Sozer, Alexis Virelizier
We construct a scalar invariant of flat principal 2-bundles over 3-manifolds, with structure 2-group , from an involutory Hopf algebra graded by . Express…
3d TQFTs and 3-manifold invariants
Kursat Sozer, Alexis Virelizier
This is an invited contribution to the 2nd edition of the Encyclopedia of Mathematical Physics. We give an overview of 3-dimensional topological quantum field theories (TQFTs) and…
Chromatic maps for finite tensor categories
Francesco Costantino, Nathan Geer, Bertrand Patureau-Mirand +1
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 t…
Hopf crossed module (co)algebras
Kursat Sozer, Alexis Virelizier
Given a crossed module , we introduce Hopf -(co)algebras which generalize Hopf algebras and Hopf group-(co)algebras. We interpret them as Hopf algebras in some symmetric mono…
Non compact (2+1)-TQFTs from non-semisimple spherical categories
Francesco Costantino, Nathan Geer, Bertrand Patureau-Mirand +1
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) pivo…
Monoidal categories graded by crossed modules and 3-dimensional HQFTs
Kursat Sozer, Alexis Virelizier
Given a crossed module , we introduce -graded monoidal categories and -fusion categories. We use spherical -fusion categories to construct (via the state sum method) 3-…