The Journal of the Indian Mathematical Society

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Finite Group Actions on Kan Complexes


Affiliations
1 Stat-Math Unit, Indian Statistical Institute, Kolkata 700108, India
2 Department of Mathematics and Statistics, Indian Institute of Technology-Kanpur, Kanpur 208016, India
     

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We study simplicial action of groups on one vertex Kan complexes. We show that every semi-direct product of the fundamental group of an one vertex Kan complex with a finite group can be simplicially realized. We also calculate the cohomology of the fixed point set of a finite p-group action on an one vertex aspherical Kan complex.

Keywords

Kan Complexes, Covering Spaces, Group Actions.
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  • Finite Group Actions on Kan Complexes

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Authors

Goutam Mukherjee
Stat-Math Unit, Indian Statistical Institute, Kolkata 700108, India
Swagata Sarkar
Stat-Math Unit, Indian Statistical Institute, Kolkata 700108, India
Debasis Sen
Department of Mathematics and Statistics, Indian Institute of Technology-Kanpur, Kanpur 208016, India

Abstract


We study simplicial action of groups on one vertex Kan complexes. We show that every semi-direct product of the fundamental group of an one vertex Kan complex with a finite group can be simplicially realized. We also calculate the cohomology of the fixed point set of a finite p-group action on an one vertex aspherical Kan complex.

Keywords


Kan Complexes, Covering Spaces, Group Actions.

References