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(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)

MINIMIZING ROOTS OF MAPS INTO THE TWO-SPHERE

Author(s):
Fenille, Marcio Colombo [1]
Total Authors: 1
Affiliation:
[1] Univ Fed Itajuba, Inst Ciencias Exatas, BR-37500904 Itajuba, MG - Brazil
Total Affiliations: 1
Document type: Journal article
Source: MATHEMATICA SCANDINAVICA; v. 111, n. 1, p. 92-106, 2012.
Web of Science Citations: 0
Abstract

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)

FAPESP's process: 07/05843-5 - Roots of maps from 2-dimensional complexes into closed surfaces
Grantee:Márcio Colombo Fenille
Support type: Scholarships in Brazil - Doctorate