MINIMIZING ROOTS OF MAPS INTO THE TWO-SPHERE

Autor(es)

Fenille, Marcio Colombo ^[1]

Afiliação do(s) autor(es)

^[1] Univ Fed Itajuba, Inst Ciencias Exatas, BR-37500904 Itajuba, MG - Brazil

• Tipo de documento: Artigo Científico
• Fonte: MATHEMATICA SCANDINAVICA; v. 111, n. 1, p. 92-106, 2012.
• Citações Web of Science: 0

Resumo

This article is a study of the root theory for maps from two-dimensional CW-complexes into the 2-sphere. Given such a map f : K -> S-2 we define two integers zeta(f) and zeta(K, d(f)), which are upper bounds for the minimal number of roots off, denote be mu(f). The number zeta(f) is only defined when f is a cellular map and zeta(K,d(f)) is defined when K is homotopy equivalent to the 2-sphere. When these two numbers are defined, we have the inequality mu(f) <= zeta(K, d(f)) <= zeta(f), where d(f) is the so-called homological degree of f. We use these results to present two very interesting examples of maps from 2-complexes homotopy equivalent to the sphere into the sphere. (AU)

• Processo FAPESP: 07/05843-5 - Raízes de funções de complexos 2-dimensionais em superfícies fechadas
• Beneficiário: Márcio Colombo Fenille
• Linha de fomento: Bolsas no Brasil - Doutorado