Components of directed spaces

Speaker(s)

Krzysztof Ziemiański

Affiliation

MIMUW - IMPAN

Date

April 5, 2018, 4:15 p.m.

Room

room 4070

Seminar

Seminar Algebraic Topology

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A directed space is a topological space with a distinguished family ofpaths . Directed spaces are used in computer science as models of concurrent programs. Unfortunately, no satisfactory analogues of classical homotopy invariants of topological spaces are known. I will present a construction of a category of components of a directed space, which is intended to be a directed analogue of the set of path-connected components of topological spaces. It has some advantages over the construction of Goubault et al.: it works in a greater generality and the component category is enriched in the homotopy category. Thus, it carries also information about higher homotopies.

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