| Full text | |
| Author(s): |
Total Authors: 2
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| Affiliation: | [1] Univ Sao Paulo, Dept Matemat, IME, BR-05311970 Sao Paulo - Brazil
[2] Univ Estadual Mato Grosso Sul UEMS, Andradina, MS - Brazil
Total Affiliations: 2
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| Document type: | Journal article |
| Source: | Central European Journal of Mathematics; v. 2, n. 1, p. 112-122, 2004. |
| Web of Science Citations: | 3 |
| Abstract | |
Given a map f : X -> Y and a Nielsen root class, there is a number associated to this root class, which is the minimal number of points among all root classes which are H-related to the given one for all homotopies H of the map f. We show that for maps between closed surfaces it is possible to deform f such that all the Nielsen root classes have cardinality equal to the minimal number if and only if either NR[f] <= 1, or NR[f] > 1 and f satisfies the Wecken property. Here NR[f] denotes the Nielsen root number. The condition "f satisfies the Wecken property is known to be equivalent to Ideg(f) l <= NR[f]I(1- x(M-2) - x(Mi)1(1 - x(M-2)) for maps between closed orientable surfaces. In the case of nonorientable surfaces the condition is A(f) <= NR[f]I(1 - x(M2) - x(Mi)/(1 - x(M-2)). Also we construct, for each integer n > 3, an example of a map f : K-n -> N from an n-dimensionally connected complex of dimension n to an n-dimensional manifold such that we cannot deform f in a way that all the Nielsen root classes reach the minimal number of points at the same time. (c) Central European Science Journals. All rights reserved. (AU) | |
| FAPESP's process: | 00/05385-8 - Algebraic, geometric and differential topology |
| Grantee: | Daciberg Lima Gonçalves |
| Support Opportunities: | Research Projects - Thematic Grants |