BIMSA > BIMSA-Tsinghua Quantum Symmetry Seminar BIMSA-Tsinghua Quantum Symmetry Seminar Quantum invariants of flat 2-bundles over 3-manifolds
Quantum invariants of flat 2-bundles over 3-manifolds
Organizers
Linzhe Huang , Zhengwei Liu , Shuang Ming , Sebastien Palcoux , Yilong Wang , Jinsong Wu
Speaker
Alexis Virelizier
Time
Thursday, May 28, 2026 10:30 AM - 12:00 PM
Venue
A3-2-301
Online
Zoom 435 529 7909 (BIMSA)
Abstract
In this talk, I will present a construction of a scalar invariant of flat principal 2-bundles over 3-manifolds, with structure 2-group G, from an involutory Hopf algebra graded by G. Using the classification of such 2-bundles via the classifying space BG, this amounts to constructing a homotopy invariant of maps from 3-manifolds to BG. The construction of the invariant relies on a combinatorial description of such maps by G-colored Heegaard diagrams. When the corresponding map to BG is nullhomotopic or, equivalently, when the associated principal G-bundle is trivializable, the invariant reduces to the Kuperberg invariant of the underlying 3-manifold.