Hostname: page-component-cd9895bd7-mkpzs Total loading time: 0 Render date: 2024-12-28T20:38:54.508Z Has data issue: false hasContentIssue false
  • English
  • Français

Graph representatives for surface maps

Published online by Cambridge University Press:  17 April 2007

MICHAEL R. KELLY
MICHAEL R. KELLY
Affiliation:
Department of Mathematics and Computer Science, Loyola University, 6363 St. Charles Avenue, New Orleans, LA 70118, USA (e-mail: kelly@loyno.edu)
Get access Rights & Permissions [Opens in a new window]

Abstract

Given a compact surface $F$ with non-empty boundary and a homotopy class of self-maps on $F$, we consider the problem of finding a representative which carries the minimal number of fixed points possible for the class. When $F$ is either the pants surface or the once punctured Möbius band this problem is solved by a graph map, where the graph is homotopy equivalent to $F$. A partial result is presented for the remaining two surfaces whose fundamental group is the free group on two generators.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 27 , Issue 3 , June 2007 , pp. 849 - 867
Copyright
2007 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)