The minimizing of the Nielsen root classes

Autor(es)

Goncalves, Daciberg L. ^[1] ; Aniz, Claudemir ^[2]

Afiliação do(s) autor(es)

^[1] Univ Sao Paulo, Dept Matemat, IME, BR-05311970 Sao Paulo - Brazil

^[2] Univ Estadual Mato Grosso Sul UEMS, Andradina, MS - Brazil

• Tipo de documento: Artigo Científico
• Fonte: Central European Journal of Mathematics; v. 2, n. 1, p. 112-122, 2004.
• Citações Web of Science: 3

Resumo

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)

• Processo FAPESP: 00/05385-8 - Topologia algébrica, geométrica e diferencial
• Beneficiário: Daciberg Lima Gonçalves
• Modalidade de apoio: Auxílio à Pesquisa - Temático