The equivariant problem of the preimage of complements of configuration-like space...
Equivariant mini-max theories, ring-valued genus, and the Borsuk-Ulam theorems
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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