A categorification of Kontsevich-Quinn finite total homotopy TQFT with application to TQFTs and once-extended TQFTs derived from discrete higher gauge theory

by João Faria Martins (Leeds)

Thursday 27 Nov 2025, 16:15 → 17:15 Europe/Berlin

H3 (Geomatikum)

Kontsevich-Quinn (Finite Total Homotopy) TQFT is a topological quantum field theory defined for any dimension $n$ of space, depending on the choice of a homotopy finite space $B$. For instance, $B$ can be the classifying space of a finite group or a finite 2-group.
In this talk, I will report on recent joint work with Tim Porter on once-extended versions of Kontsevich-Quinn TQFT, taking values in the symmetric monoidal bicategory of groupoids, linear profunctors, and natural transformations between linear profunctors. The construction works in all dimensions, yielding (0,1,2)-, (1,2,3)-, and (2,3,4)-extended TQFTs, given a homotopy finite space $B$. I will show how to compute these once-extended TQFTs when $B$ is the classifying space of a homotopy 2-type, represented by a crossed module of groups.
Time permitting, I will address the twice-extended TQFTs also arising, as well as the ensuing representations of motion groups. 

Reference:

Faria Martins J, Porter T: "A categorification of Quinn's finite total homotopy TQFT with application to TQFTs and once-extended TQFTs derived from strict omega-groupoids." arXiv:2301.02491 [math.CT]