| Full text | |
| Author(s): |
de Mattos, Denise
[1]
;
Pergher, Pedro L. Q.
[2]
;
dos Santos, Edivaldo L.
[2]
;
Singh, Mahender
[3]
Total Authors: 4
|
| Affiliation: | [1] Univ Sao Paulo, Inst Ciencias Matemat & Comp, Dept Matemat, CP 668, BR-13560970 Sao Carlos, SP - Brazil
[2] Univ Fed Sao Carlos, Dept Matemat, Ctr Ciencias Exatas & Tecnol, CP 676, BR-13565905 Sao Carlos, SP - Brazil
[3] Indian Inst Sci Educ & Res IISER Mohali, Sect 81, PO Manauli, Manauli 140306, Punjab - India
Total Affiliations: 3
|
| Document type: | Journal article |
| Source: | Topology and its Applications; v. 202, p. 7-20, APR 1 2016. |
| Web of Science Citations: | 4 |
| Abstract | |
Let E -> B be a fiber bundle and E' -> B be a vector bundle. Let G be a compact group acting fiber preservingly and freely on both E and E' - 0, where 0 is the zero section of E' -> B. Let f : E -> E' be a fiber preserving G-equivariant map, and let Z(f) = [x is an element of E vertical bar f (x) = 0] be the zero set of f. It is an interesting problem to estimate the dimension of the set Z(f). In 1988, Dold {[}5] obtained a lower bound for the cohomological dimension of the zero set Z(f) when E -> B is the sphere bundle associated with a vector bundle which is equipped with the antipodal action of G = Z/2. In this paper, we generalize this result to products of finitely many spheres equipped with the diagonal antipodal action of Z/2. We also prove a Bourgin-Yang type theorem for products of spheres equipped with the diagonal antipodal action of Z/2. (C) 2015 Elsevier B.V. All rights reserved. (AU) | |
| FAPESP's process: | 13/10353-8 - Separation theorems and properties of the general position in generalized manifolds |
| Grantee: | Edivaldo Lopes dos Santos |
| Support Opportunities: | Regular Research Grants |
| FAPESP's process: | 13/24845-0 - On Lusternik-Schnirelmann category, ideal-value genus and global classification of isolated singularities |
| Grantee: | Denise de Mattos |
| Support Opportunities: | Regular Research Grants |
| FAPESP's process: | 12/24454-8 - Algebraic, geometric and differential topology |
| Grantee: | Daciberg Lima Gonçalves |
| Support Opportunities: | Research Projects - Thematic Grants |