Estimation of the Number of Roots on the Complement

Yang Ki-Yeol; Yang Ki-Yeol

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P-ISSN3059-0604
E-ISSN3059-1309
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Vol.13 No.1

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Estimation of the Number of Roots on the Complement

Journal of the Korean Society of Mathematical Education Series B: Theoretical Mathematics and Pedagogical Mathematics / Journal of the Korean Society of Mathematical Education Series B: Theoretical Mathematics and Pedagogical Mathematics, (P)3059-0604; (E)3059-1309

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

Yang Ki-Yeol

Yang, K. (2006). Estimation of the Number of Roots on the Complement, 13(1), 11-18.

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Abstract

Let f : (X, A) ${\rightarrow}$ (Y, B) be a map of pairs of compact polyhedra. A surplus Nielsen root number $SN(f;X\;{\backslash}\;A,\;c)$ 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 $SN(f;X\;{\backslash}\;A,\;c)$ can be realized without by-passing condition.

keywords: Root, surplus Nielsen root number

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Article Contents

Vol.13 No.1

Estimation of the Number of Roots on the Complement

Abstract

Journal of the Korean Society of Mathematical Education Series B: Theoretical Mathematics and Pedagogical Mathematics