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XI Brazilian Meeting of Topology
August 3-7, 1998
IGCE - Universidade Estadual Paulista - UNESP
Rio Claro, S.P., Brazil

Organizers
Joao Peres Vieira, Marcelo Jose Saia, Oziride Manzoli Neto, Suely Druck, Alice Kimie Miwa Libardi, Izabel Cristina Rossini

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Index bounds and self-mappings of 2-complexes
by
Michael R. Kelly
Loyola University-New Orleans , LA USA

A pseudo-Anosov homeomorphism of a compact surface has the property that the index of each fixed point is bounded above by 1 and below by 2\chi-1, where \chi denotes the Euler characteristic of the surface. In addition, the following inequality holds:
| L(h)-\chi(F)| <= NF(h) - \chi(F)  ,
where L(h) is the Lefschetz number and NF(h) the number of fixed points. In this talk we discuss two generalizations regarding arbitrary continuous self-mappings of surfaces. One is to the class of surface self-mappings which are fixed point minimal (relative to their homotopy class). When the surface has non-empty boundary, the same index bounds hold, as does the above inequality. Secondly, for an arbitrary map we obtain the same conclusions when fixed points are replaced by Nielsen-classes of fixed points. As a consequence we obtain a partial generalization for fixed point minimal self-mappings of 2-complexes.

Date received: May 26, 1998

Copyright © 1998 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cabo-05.