pith. sign in

arxiv: math/0005291 · v1 · submitted 2000-05-31 · 🧮 math.GT · math.QA

Homotopy field theory in dimension 3 and crossed group-categories

classification 🧮 math.GT math.QA
keywords dimensionalhomotopycrossedcategoryfieldhqftintroducemodular
0
0 comments X
read the original abstract

A 3-dimensional homotopy quantum field theory (HQFT) can be described as a TQFT for surfaces and 3-cobordisms endowed with homotopy classes of maps into a given space. For a group $\pi$, we introduce a notion of a modular crossed $\pi$-category and show that such a category gives rise to a 3-dimensional HQFT with target space $K(\pi,1)$. This includes numerical invariants of 3-dimensional $\pi$-manifolds and a 2-dimensional homotopy modular functor. We also introduce and discuss a parallel notion of a quasitriangular crossed Hopf $\pi$-coalgebra.

This paper has not been read by Pith yet.

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Forward citations

Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Characterizing bulk properties of gapped phases by smeared boundary conformal field theories: Role of duality in unusual ordering

    hep-th 2026-05 unverdicted novelty 7.0

    Gapped phases dual to massless RG flows exhibit unusual structures outside standard boundary CFT modules and typically break non-group-like symmetries, characterized via smeared boundary CFTs with an example in the tr...

  2. Characterizing bulk properties of gapped phases by smeared boundary conformal field theories: Role of duality in unusual ordering

    hep-th 2026-05 unverdicted novelty 6.0

    Gapped phases dual to massless RG flows in 2D CFTs exhibit unusual ordering via spontaneous breaking of non-group-like symmetries and are characterized using smeared boundary CFTs applied to smeared Ishibashi states.