A model structure via orbit spaces for equivariant homotopy

Erdal M. A., Güçlükan İlhan A.

JOURNAL OF HOMOTOPY AND RELATED STRUCTURES, vol.14, no.4, pp.1131-1141, 2019 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 14 Issue: 4
  • Publication Date: 2019
  • Doi Number: 10.1007/s40062-019-00241-4
  • Journal Name: JOURNAL OF HOMOTOPY AND RELATED STRUCTURES
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.1131-1141
  • Keywords: Equivariant homotopy, Orbit space, Model structure
  • Dokuz Eylül University Affiliated: Yes

Abstract

Let G be discrete group and F be a collection of subgroups of G. We show that there exists a left induced model structure on the category of right G-simplicial sets, in which the weak equivalences and cofibrations are the maps that induce weak equivalences and cofibrations on H-orbits for all H in F. This gives a model categorical criterion for maps that induce weak equivalences on H-orbits to be weak equivalences in the F-model structure.