The minimizing of the Nielsen root classes

• Autorzy: Daciberg Gonçalves , Claudemir Aniz
• Języki publikacji: EN

Abstrakty

EN

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 N R[f]≤1, or N R[f]>1 and f satisfies the Wecken property. Here N R[f] denotes the Nielsen root number. The condition “f satisfies the Wecken property is known to be equivalent to |deg(f)|≤N R[f]/(1−χ(M 2)−χ(M 10/(1−χ(M 2)) for maps between closed orientable surfaces. In the case of nonorientable surfaces the condition is A(f)≤N R[f]/(1−χ(M 2)−χ(M 2)/(1−χ(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.

Słowa kluczowe

EN

Nielsen root classes; Absolut degree; Wecken property; closed surfaces; complex; 55M20; 57M12; 20F99

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2004
• Tom: 2
• Numer: 1
• Strony: 112-122

Daty

wydano

2004-03-01

online

2004-03-01

Twórcy

autor

Daciberg Gonçalves

• IME-USP

autor

Claudemir Aniz

• Universidade Estadual de Mato Grosso do Sul-UEMS

Bibliografia

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Identyfikatory

DOI

10.2478/BF02475955