Index bounds for surface self-mappings
by
Michael R. Kelly
Loyola University-New Orleans

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. 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. A generalization to self-maps of 2-complexes will also be discussed.

Date received: February 8, 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 # caas-39.