Inessential directed maps and directed homotopy equivalences

@article{Raussen2021InessentialDM,
  title={Inessential directed maps and directed homotopy equivalences},
  author={Martin Raussen},
  journal={Proceedings of the Royal Society of Edinburgh: Section A Mathematics},
  year={2021},
  volume={151},
  pages={1383 - 1406}
}
  • M. Raussen
  • Published 21 June 2019
  • Mathematics
  • Proceedings of the Royal Society of Edinburgh: Section A Mathematics
A directed space is a topological space $X$ together with a subspace $\vec {P}(X)\subset X^I$ of directed paths on $X$. A symmetry of a directed space should therefore respect both the topology of the underlying space and the topology of the associated spaces $\vec {P}(X)_-^+$ of directed paths between a source ($-$) and a target ($+$)—up to homotopy. If it is, moreover, homotopic to the identity map—in a directed sense—such a symmetry will be called an inessential d-map, and the paper explores… 
1 Citations

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