Bounds on the fixed point indices for self-maps of certain simplicial complexes

✍ Scribed by Michael R. Kelly

• Publisher: Elsevier Science
• Year: 2000
• Tongue: English
• Weight: 172 KB
• Volume: 108
• Category: Article
• ISSN: 0166-8641
• DOI: 10.1016/s0166-8641(99)00131-5

✦ Synopsis

This paper gives a generalization of results concerning fixed point index bounds for self-mappings of surfaces with boundary. Consider the class of finite polyhedra which have no local separating points and are homotopy equivalent to a one-complex. Given a member X of this class and a fixed point minimal self-mapping f : X → X it is shown that the index of each fixed point is bounded above by 1, and also that for any collection of those with index less than -1 their total index is bounded below by 2χ -N, where N denotes the number of fixed points in the collection.