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Configuration spaces and directed paths on the final precubical set

Volume 257 / 2022

Jakub Paliga, Krzysztof Ziemiański Fundamenta Mathematicae 257 (2022), 229-263 MSC: Primary 55P35, 68Q85; Secondary 55P15. DOI: 10.4064/fm114-9-2021 Published online: 3 January 2022

Abstract

The main goal of this paper is to prove that the space of directed loops on the final precubical set is homotopy equivalent to the “total” configuration space of points on the plane; by “total” we mean that any finite number of points in the configuration is allowed. We also provide several applications: we define new invariants of precubical sets, prove that directed path spaces on any precubical complex have the homotopy types of CW-complexes and construct certain presentations of configuration spaces of points on the plane as nerves of categories.

Authors

  • Jakub PaligaFaculty of Mathematics, Informatics and Mechanics
    University of Warsaw
    Banacha 2
    02-097 Warszawa, Poland
    e-mail
  • Krzysztof ZiemiańskiFaculty of Mathematics, Informatics and Mechanics
    University of Warsaw
    Banacha 2
    02-097 Warszawa, Poland
    e-mail

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