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A bound on the fixed-point index for surface mappings

Published online by Cambridge University Press:  01 December 1997

MICHAEL R. KELLY
MICHAEL R. KELLY
Affiliation:
Department of Mathematics and Computer Science, Loyola University, New Orleans, Louisiana, 70118, USA
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Abstract

In this paper we consider the class of surface mappings consisting of those maps which have the least number of fixed points possible among all maps in their homotopy class. When the surface has non-empty boundary, we show that for mappings in this class the index of a fixed point is bounded above by $1$ and below by $2\chi -1$. This generalizes a well known result for pseudo-Anosov homeomorphisms. A proof of a Jiang–Guo type inequality is also given.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 17 , Issue 6 , December 1997 , pp. 1393 - 1408
Copyright
1997 Cambridge University Press

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