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

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.