Estimation of the Number of Roots on the Complement

한국수학교육학회지시리즈B:순수및응용수학 / Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, (P)1226-0657; (E)2287-6081

2006, v.13 no.1, pp.11-18

Yang Ki-Yeol (DEPARTMENT OF MATHEMATICS, EDUCATION, SUNCHON NATIONAL UNIVERSITY)

Yang Ki-Yeol. (2006). ESTIMATION OF THE NUMBER OF ROOTS ON THE COMPLEMENT. 한국수학교육학회지시리즈B:순수및응용수학, 13(1), 11-18.

복사

Abstract

Let f : (X, A) <TEX>${\rightarrow}$</TEX> (Y, B) be a map of pairs of compact polyhedra. A surplus Nielsen root number <TEX>$SN(f;X\;{\backslash}\;A,\;c)$</TEX> is defined which is lower bound for the number of roots on X \ A for all maps in the homotopy class of f. It is shown that for many pairs this lower bound is the best possible one, as <TEX>$SN(f;X\;{\backslash}\;A,\;c)$</TEX> can be realized without by-passing condition.

keywords: Root, surplus Nielsen root number

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Vol.13 No.1

ESTIMATION OF THE NUMBER OF ROOTS ON THE COMPLEMENT

Estimation of the Number of Roots on the Complement

Abstract

한국수학교육학회지시리즈B:순수및응용수학