MINIMIZING ROOTS OF MAPS INTO THE TWO-SPHERE

Author(s)

Fenille, Marcio Colombo ^[1]

Affiliation

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

• 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 Opportunities: Scholarships in Brazil - Doctorate