Stratified spaces, Directed Algebraic Topology, and State-Sum TQFTs
arXiv:1807.07910
Abstract
We apply the theory of directed topology developed by Grandis [9, 10] to the study of stratified spaces by describing several ways in which a stratification or a stratification with orientations on the strata can be used to produce a related directed space structure. This description provides a setting for the constructions of state-sum TQFTs with defects of [5, 8], which we extend to a similar construction of a Dijkgraaf- Witten type TQFT in the case where the defects (lower dimensional strata) are not sources or targets, but sources on one side and targets on the other, according to an orientation convention.
References in corpus (6)
- On the Unicity of the Homotopy Theory of Higher Categories
- Directed homotopy theory, I. The fundamental category
- Transversal homotopy theory
- Moves on Filtered PL Manifolds and Stratified PL Spaces
- On 2-Dimensional Dijkgraaf-Witten Theory with Defects
- Dijkgraaf-Witten Type Invariants of Seifert Surfaces in 3-Manifolds