Volume 17, issue 5 (2013)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 28
Issue 5, 1995–2482
Issue 4, 1501–1993
Issue 3, 1005–1499
Issue 2, 497–1003
Issue 1, 1–496

Volume 27, 9 issues

Volume 26, 8 issues

Volume 25, 7 issues

Volume 24, 7 issues

Volume 23, 7 issues

Volume 22, 7 issues

Volume 21, 6 issues

Volume 20, 6 issues

Volume 19, 6 issues

Volume 18, 5 issues

Volume 17, 5 issues

Volume 16, 4 issues

Volume 15, 4 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 5 issues

Volume 11, 4 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 3 issues

Volume 7, 2 issues

Volume 6, 2 issues

Volume 5, 2 issues

Volume 4, 1 issue

Volume 3, 1 issue

Volume 2, 1 issue

Volume 1, 1 issue

The Journal
About the Journal
Editorial Board
Editorial Procedure
Subscriptions
 
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
 
ISSN 1364-0380 (online)
ISSN 1465-3060 (print)
Author Index
To Appear
 
Other MSP Journals
About the homological discrete Conley index of isolated invariant acyclic continua

Luis Hernández-Corbato, Patrice Le Calvez and Francisco R Ruiz del Portal

Geometry & Topology 17 (2013) 2977–3026
Abstract

This article includes an almost self-contained exposition on the discrete Conley index and its duality. We work with a locally defined homeomorphism f in d and an acyclic continuum X, such as a cellular set or a fixed point, invariant under f and isolated. We prove that the trace of the first discrete homological Conley index of f and X is greater than or equal to 1 and describe its periodical behavior. If equality holds then the traces of the higher homological indices are 0. In the case of orientation-reversing homeomorphisms of 3, we obtain a characterization of the fixed point index sequence {i(fn,p)}n1 for a fixed point p which is isolated as an invariant set. In particular, we obtain that i(f,p) 1. As a corollary, we prove that there are no minimal orientation-reversing homeomorphisms in 3.

Keywords
fixed point index, Conley index, filtration pairs
Mathematical Subject Classification 2010
Primary: 37B30, 37C25, 54H25
References
Publication
Received: 6 February 2013
Revised: 24 June 2013
Accepted: 26 June 2013
Published: 17 October 2013
Proposed: Yasha Eliashberg
Seconded: Leonid Polterovich, Steve Ferry
Authors
Luis Hernández-Corbato
Departamento de Geometría y Topología
Universidad Complutense de Madrid
Plaza de Ciencias 3
28040 Madrid
Spain
Patrice Le Calvez
Institut de Mathematiques de Jussieu
Université Pierre et Marie Curie
UMR 7586 CNRS
Case 247, 4, place Jussieu
75252 Paris
France
Francisco R Ruiz del Portal
Departamento de Geometría y Topología
Universidad Complutense de Madrid
Plaza de Ciencias 3
28040 Madrid
Spain
http://www.mat.ucm.es/~rrportal/