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Equivariant deformations with applications to Nielsen Borsuk-Ulam theory

Grant number: 20/10874-1
Support Opportunities:Regular Research Grants
Start date: January 01, 2021
End date: June 30, 2023
Field of knowledge:Physical Sciences and Mathematics - Mathematics - Geometry and Topology
Principal Investigator:Thaís Fernanda Mendes Monis
Grantee:Thaís Fernanda Mendes Monis
Host Institution: Instituto de Geociências e Ciências Exatas (IGCE). Universidade Estadual Paulista (UNESP). Campus de Rio Claro. Rio Claro , SP, Brazil
Associated researchers: Peter Ngai-Sing Wong

Abstract

Let G be a finite group acting on spaces X and Y and let B be a invariant subset of Y. Given a G-map from X to Y, one can ask if the given map is G-homotopic to a map with image off B. In this work, we propose to study this problem via equivariant obstruction theory using Bredon cohomology with local coefficients. In the particular case where B is a point fixed by G, the problem is an equivariant root problem. Another application is the study of coincidences of Borsuk-Ulam type recently studied by Cotrim and Vendrúsculo. (AU)

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