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Coarse homotopy groups

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  • Paul D. Mitchener
  • Behnam Norouzizadeh
  • Thomas Schick

Abstract

In this note on coarse geometry we revisit coarse homotopy. We prove that coarse homotopy indeed is an equivalence relation, and this in the most general context of abstract coarse structures. We introduce (in a geometric way) coarse homotopy groups. The main result is that the coarse homotopy groups of a cone over a compact simplicial complex coincide with the usual homotopy groups of the underlying compact simplicial complex. To prove this we develop geometric triangulation techniques for cones which we expect to be of relevance also in different contexts.

Suggested Citation

  • Paul D. Mitchener & Behnam Norouzizadeh & Thomas Schick, 2020. "Coarse homotopy groups," Mathematische Nachrichten, Wiley Blackwell, vol. 293(8), pages 1515-1533, August.
    • Handle: RePEc:bla:mathna:v:293:y:2020:i:8:p:1515-1533
    DOI: 10.1002/mana.201800523
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