Volume 17, issue 5 (2013)

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

Volume 26
Issue 2, 477–936
Issue 1, 1–476

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 Interests
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
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

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.

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