3 papers
math.QA2026
A geometrical description of untwisted 3d Dijkgraaf-Witten TQFT with defects
João Faria Martins, Catherine Meusburger
We give a simple, geometric and explicit construction of 3d untwisted Dijkgraaf-Witten theory with defects of all codimensions. It is given as a symmetric monoidal functor from a d…
math.CT2025
A categorification of Quinn's finite total homotopy TQFT with application to TQFTs and once-extended TQFTs derived from strict omega-groupoids
João Faria Martins, Timothy Porter
We first revisit the construction of Quinn's finite total homotopy TQFT, which depends on the choice of a homotopy finite space, . This constitutes a vast generalis…
math-ph2024
Exactly solvable models for 2+1D topological phases derived from crossed modules of semisimple Hopf algebras
Vincent Koppen, João Faria Martins, Paul Purdon Martin
We define an exactly solvable model for 2+1D topological phases of matter on a triangulated surface derived from a crossed module of semisimple finite-dimensional Hopf algebras, th…