| Full text | |
| Author(s): |
Goncalves, Daciberg Lima
;
Guaschi, John
;
Laass, Vinicius Casteluber
Total Authors: 3
|
| Document type: | Journal article |
| Source: | TOPOLOGICAL METHODS IN NONLINEAR ANALYSIS; v. 60, n. 2, p. 26-pg., 2022-12-01. |
| Abstract | |
Let M be a topological space that admits a free involution r, and let N be a topological space. A homotopy class beta is an element of [M, N] is said to have the Borsuk-Ulam property with respect to r if for every representative map f : M -> N of beta, there exists a point x is an element of M such that f (r(x)) = f (x). In this paper, we determine the homotopy class of maps from the 2-torus T2 to the Klein bottle K2 that possess the Borsuk-Ulam property with respect to any free involution of T2 for which the orbit space is K2. Our results are given in terms of a certain family of homomorphisms involving the fundamental groups of T2 and K2. This completes the analysis of the Borsuk-Ulam problem for the case M = T2 and N = K2, and for any free involution r of T2. (AU) | |
| FAPESP's process: | 16/24707-4 - Algebraic, geometric and differential topology |
| Grantee: | Daciberg Lima Gonçalves |
| Support Opportunities: | Research Projects - Thematic Grants |