Z(2)-bordism and the Borsuk-Ulam Theorem

Author(s)

Crabb, M. C. ^[1] ; Goncalves, D. L. ^[2] ; Libardi, A. K. M. ^[3] ; Pergher, P. L. Q. ^[4]

Affiliation

^[1] Univ Aberdeen, Dept Math, Aberdeen AB24 3UE - Scotland

^[2] Univ Sao Paulo, Dept Matemat, IME, Caixa Postal 66281, BR-05314970 Sao Paulo, SP - Brazil

^[3] IGCE UNESP, Dept Matemat, BR-13506900 Rio Claro, SP - Brazil

^[4] Univ Fed Sao Carlos, Dept Matemat, Caixa Postal 676, BR-13565905 Sao Carlos, SP - Brazil

• Document type: Journal article
• Source: MANUSCRIPTA MATHEMATICA; v. 150, n. 3-4, p. 371-381, JUL 2016.
• Web of Science Citations: 0

Abstract

The purpose of this work is to classify, for given integers , the bordism class of a closed smooth -manifold with a free smooth involution with respect to the validity of the Borsuk-Ulam property that for every continuous map there exists a point such that . We will classify a given free -bordism class according to the three possible cases that (a) all representatives of satisfy the Borsuk-Ulam property; (b) there are representatives and of such that satisfies the Borsuk-Ulam property but does not; (c) no representative of satisfies the Borsuk-Ulam property. (AU)

• FAPESP's process: 12/24454-8 - Algebraic, geometric and differential topology
• Grantee: Daciberg Lima Gonçalves
• Support Opportunities: Research Projects - Thematic Grants