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- W2753998542 abstract "This short note introduces a notion of homotopy equivalence and of directed topological complexity (which elaborates on the notion that can be found in e.g. Farber's book) which have a number of desirable joint properties. In particular, being dihomotopically equivalent implies having bisimilar natural homologies (defined in Dubut et al. 2015). Also, under mild conditions, topological complexity is an invariant of our homotopy equivalence and having a topological complexity equal to one is (under these conditions) equivalent to being dihomotopy equivalent to a point (i.e., to being dicontractible, as in the undirected case). It still remains to compare this notion with the notion introduced in Dubut et al. 2016, which has lots of good properties as well. For now, it seems that for reasonable spaces, this new proposal of homotopy equivalence identifies more spaces than the one of Dubut et al. 2016." @default.
- W2753998542 created "2017-09-25" @default.
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- W2753998542 date "2017-09-17" @default.
- W2753998542 modified "2023-09-27" @default.
- W2753998542 title "On directed homotopy equivalences and a notion of directed topological complexity." @default.
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