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ISSN : 1226-0657

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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: The Pure and Applied Mathematics / 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
Yang, K. (2006). Estimation of the Number of Roots on the Complement. Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, 13(1), 11-18.
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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.

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Root, surplus Nielsen root number

Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics

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