Non-symmetric and parametrized versions of the Borsuk-Ulam theorem

• Grant number: 06/03932-8
• Support Opportunities: Regular Research Grants
• Start date: October 01, 2006
• End date: September 30, 2008
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Denise de Mattos
• Grantee: Denise de Mattos
• Host Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil

Abstract

Our objective in this project is to give continuity to the studies of new versions of the Borsuk-Ulam theorem, initiated during my doctoral research. Particularly, we will be interested in studying non-symmetric and parametrized versions of this famous theorem. The non-symmetric version, considers the problem of to estimate the cohomological dimension of the set A(f) of relative (H,G)-coincidence points for maps f:X => Y^{k}, where X is a compact topological space, G is a finite group, H is subgroup of G and Y^{k} is a k-dimensional CW-complex. We intend to establish one parametrized version of the Borsuk-Ulam theorem, which extendsthe result proved by Koikara and Mukerjee (Topology Appl., 1995), for the cyclic group G=Z_{p}. Specifically, we will be considering in the parametrized problem a fiber E=> B, whosefiber is a product of spheres S^{m}xS^{n}. (AU)