Fixed Point Theory and Applications
Volume 2006 (2006), Article ID 87657, 8 pages
doi:10.1155/FPTA/2006/87657

Fixed point indices and manifolds with collars

Chen-Farng Benjamin1 and Daniel Henry Gottlieb2

1705 Sugar Hill Drive, West Lafayette 47906, IN, USA
2Mathematics Department, Purdue University, West Lafayette 47907, IN, USA

Received 7 December 2004; Revised 25 April 2005; Accepted 24 July 2005

Copyright © 2006 Chen-Farng Benjamin and Daniel Henry Gottlieb. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

This paper concerns a formula which relates the Lefschetz number L(f) for a map f:M→M′ to the fixed point index I(f) summed with the fixed point index of a derived map on part of the boundary of ∂M. Here M is a compact manifold and M′ is M with a collar attached.