The Pure and Applied Mathematics (한국수학교육학회지시리즈B:순수및응용수학)

Korean Society of Mathematical Education (한국수학교육학회)
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ESTIMATION OF THE NUMBER OF ROOTS ON THE COMPLEMENT

  • Yang Ki-Yeol (DEPARTMENT OF MATHEMATICS, EDUCATION, SUNCHON NATIONAL UNIVERSITY)
  • Published : 2006.02.01
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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.

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