Stratified spaces, directed algebraic topology, and state-sum TQFTs. (English) Zbl 1494.55019
The authors apply the theory of directed topology developed by Grandis [M. Grandis, Cah. Topol. Géom. Différ. Catég. 44, No. 4, 281–316 (2003; Zbl 1059.55009) and Directed algebraic topology. Models of non-reversible worlds. Cambridge: Cambridge University Press (2009; Zbl 1176.55001)] 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, which they 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.
Reviewer: Philippe Gaucher (Paris)
MSC:
| 55P99 | Homotopy theory |
| 57R56 | Topological quantum field theories (aspects of differential topology) |
| 57Q99 | PL-topology |
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