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Lefschetz numbers of periodic orbits of pseudo-Anosov homeomorphisms

Published online by Cambridge University Press:  24 October 2008

John Guaschi
John Guaschi
Affiliation:
Centre de Recerca Matemàtica, Institut d'estudis Catalans, Apartat 50, 08193 Bellaterra (Barcelona), Spain
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Abstract

Given a surface homeomorphism isotopic to the identity which is pseudo-Anosov relative to a finite set, we show that the sum of the Lefschetz numbers of periodic points of any period greater than one is non-negative. If this period is odd and greater than a number which depends only on the surface, the sum is zero. If we consider sequences of periods such that each element is twice that of its predecessor, then this sum is increasing beyond a certain point also depending on the surface. As a corollary, for each periodic orbit contained within the boundary of the surface there exists one of the same period contained in the interior.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 115 , Issue 1 , January 1994 , pp. 121 - 132
Copyright
Copyright © Cambridge Philosophical Society 1994

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