Borsuk-Ulam theorem for filtered spaces

Author(s)

Biasi, Carlos ^[1] ; Libardi, Alice Kimie Miwa ^[2] ; de Mattos, Denise ^[1] ; Ura, Sergio Tsuyoshi ^[2]

Affiliation

^[1] Sao Paulo Univ USP, Dept Matemat, Inst Ciencias Matemat & Comp, Campus Sao Carlos, BR-13560970 Sao Carlos, SP - Brazil

^[2] Sao Paulo State Univ Unesp, Inst Geosci & Exact Sci, Dept Matemat, BR-13506700 Rio Claro, SP - Brazil

• Document type: Journal article
• Source: FORUM MATHEMATICUM; v. 33, n. 2, p. 419-426, MAR 2021.
• Web of Science Citations: 0

Abstract

Let X and Y be pathwise connected and paracompact Hausdorff spaces equipped with free involutions T : X -> X and S : Y -> Y, respectively. Suppose that there exists a sequence (X-i, T-i) (hi) -> (Xi+1, Ti+1) for 1 <= i <= k, where, for each i, X-i is a pathwise connected and paracompact Hausdorff space equipped with a free involution T-i, such that Xk+1 = X, and h(i) : X-i -> Xi+1 is an equivariant map, for all 1 <= i <= k. To achieve Borsuk-Ulam-type theorems, in several results that appear in the literature, the involved spaces X in the statements are assumed to be cohomological n-acyclic spaces. In this paper, by considering a more wide class of topological spaces X (which are not necessarily cohomological n-acyclic spaces), we prove that there is no equivariant map f : (X, T) -> (Y, S) and we present some interesting examples to illustrate our results. (AU)

• FAPESP's process: 16/24707-4 - Algebraic, geometric and differential topology
• Grantee: Daciberg Lima Gonçalves
• Support Opportunities: Research Projects - Thematic Grants
• FAPESP's process: 18/17240-8 - Persistent Homology of functional data in aleatory metric spaces
• Grantee: Sergio Tsuyoshi Ura
• Support Opportunities: Scholarships in Brazil - Post-Doctoral