A minimum theorem for the relative root Nielsen number

Ki-Yeol Yang; Xuezhi Zhao

Communications of the
Korean Mathematical Society CKMS

ISSN(Print) 1225-1763 ISSN(Online) 2234-3024

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Commun. Korean Math. Soc. 2004; 19(1): 159-167

Printed March 1, 2004

A minimum theorem for the relative root Nielsen number

Ki-Yeol Yang, Xuezhi Zhao

Sunchon National University, Capital Normal University

Abstract

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Abstract

In [1], a relative root Nielsen number $N_{rel} (f;c)$ is introduced which is a homotopy invariant lower bound for the number of roots at $c \in Y$ for a map of pairs of spaces $f:(X,A) \to (Y,B)$. In this paper, we obtain a minimum theorem for $N_{rel} (f;c)$ under some new assumptions on the spaces and maps which are different from those in [1].

Keywords: root, Nielsen number, relative map

MSC numbers: 55M20