| Full text | |
| Author(s): |
Goncalves, Daciberg Lima
;
Guaschi, John
Total Authors: 2
|
| Document type: | Journal article |
| Source: | SCIENCE CHINA-MATHEMATICS; v. 60, n. 9, p. 1561-1574, SEP 2017. |
| Web of Science Citations: | 2 |
| Abstract | |
In this paper, we explore the fixed point theory of n-valued maps using configuration spaces and braid groups, focusing on two fundamental problems, the Wecken property, and the computation of the Nielsen number. We show that the projective plane (resp. the 2-sphere S-2) has the Wecken property for n-valued maps for all n a a{''}center dot (resp. all n 3). In the case n = 2 and S-2, we prove a partial result about the Wecken property. We then describe the Nielsen number of a non-split n-valued map of an orientable, compact manifold without boundary in terms of the Nielsen coincidence numbers of a certain finite covering q: XI, -> X with a subset of the coordinate maps of a lift of the n-valued split map phi circle q: (X) over cap-circle X. (AU) | |
| FAPESP's process: | 12/24454-8 - Algebraic, geometric and differential topology |
| Grantee: | Daciberg Lima Gonçalves |
| Support Opportunities: | Research Projects - Thematic Grants |