A parametrized version of the Borsuk-Ulam theorem

Author(s)

Nelson Antonio Silva

• Document type: Master's Dissertation
• Press: São Carlos.
• Institution: Universidade de São Paulo (USP). Instituto de Ciências Matemáticas e de Computação (ICMC/SB)
• Defense date: 2011-03-18

Examining board members

Denise de Mattos; Thiago de Melo; Pedro Luiz Queiroz Pergher

• Advisor: Denise de Mattos

Abstract

The classical Borsuk-Ulam Theorem gives information about maps \'S POT. n\' \'ARROW\' \'R POT. n\' where \'S POT. n\' has a free action of the cyclic group \'Z IND. 2\'. The theorem states that there is at least one orbit which is sent to a single point in \'R POT. n\'. Dold [9] extended this problem to a fibre-wise setting, by considering maps f : S (E) \'ARROW\' \' E POT. prime\' which preserve fibres; here, S (E) denotes the total space of the sphere bundle associated over B to a vector bundle E \'ARROW\' B and \'E POT. prime\' \'ARROW\' B is other vector bundle over B. The purpose of this work is to prove this version of the Borsuk-Ulam theorem obtained by A. Dold, called parametrized version of the Borsuk-Ulam theorem. We also prove a cohomological generalization of this problem (AU)

• FAPESP's process: 08/07198-2 - A parametrized version of the Borsuk-Ulam Theorem
• Grantee: Nelson Antonio Silva
• Support Opportunities: Scholarships in Brazil - Master