Homotopy field theory in dimension 2 and group-algebras
| dc.creator | Turaev, Vladimir | |
| dc.date | 1999-10-04 | |
| dc.date.accessioned | 2026-07-07T05:31:01Z | |
| dc.date.available | 2026-07-07T05:31:01Z | |
| dc.description | We apply the idea of a topological quantum field theory (TQFT) to maps from manifolds into topological spaces. This leads to a notion of a (d+1)-dimensional homotopy quantum field theory (HQFT) which may be described as a TQFT for closed d-dimensional manifolds and (d+1)-dimensional cobordisms endowed with homotopy classes of maps into a given space. For a group $π$, we introduce cohomological HQFT's with target $K(π,1)$ derived from cohomology classes of $π$ and its subgroups of finite index. The main body of the paper is concerned with (1+1)-dimensional HQFT's. We classify them in terms of so called crossed group-algebras. In particular, the cohomological (1+1)-dimensional HQFT's over a field of characteristic 0 are classified by simple crossed group-algebras. We introduce two state sum models for (1+1)-dimensional HQFT's and prove that the resulting HQFT's are direct sums of rescaled cohomological HQFT's. We also discuss a version of the Verlinde formula in this setting. | |
| dc.identifier | https://arxiv.org/abs/math/9910010 | |
| dc.identifier | http://arxiv.org/abs/math/9910010 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/79193 | |
| dc.subject | Quantum Algebra | |
| dc.subject | Algebraic Topology | |
| dc.title | Homotopy field theory in dimension 2 and group-algebras | |
| dc.type | text |