Structured Topological Field Theories via Crossed Simplicial Groups
Abstract
We show how the framework of crossed simplicial groups may be used to provide a classification of topological field theories on open cobordism categories defined by reductions of the structure group to a planar Lie group. Such theories are equivalent to algebras equipped with a group action and a nondegenerate trace satisfying certain invariance requirements which generalize the notion of a frobenius algebra.
 Publication:

arXiv eprints
 Pub Date:
 March 2016
 DOI:
 10.48550/arXiv.1603.02614
 arXiv:
 arXiv:1603.02614
 Bibcode:
 2016arXiv160302614S
 Keywords:

 Mathematics  Category Theory;
 Mathematics  Algebraic Topology;
 55N22
 EPrint:
 46 pages, 7 figures