Volume 9, issue 1 (2009)

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

Volume 17
Issue 6, 3213–3852
Issue 5, 2565–3212
Issue 4, 1917–2564
Issue 3, 1283–1916
Issue 2, 645–1281
Issue 1, 1–643

Volume 16, 6 issues

Volume 15, 6 issues

Volume 14, 6 issues

Volume 13, 6 issues

Volume 12, 4 issues

Volume 11, 5 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 4 issues

Volume 7, 4 issues

Volume 6, 5 issues

Volume 5, 4 issues

Volume 4, 2 issues

Volume 3, 2 issues

Volume 2, 2 issues

Volume 1, 2 issues

The Journal
About the Journal
Subscriptions
Editorial Board
Editorial Interests
Editorial Procedure
Submission Guidelines
Submission Page
Author Index
To Appear
ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Minimal entropy and geometric decompositions in dimension four

Pablo Suárez-Serrato

Algebraic & Geometric Topology 9 (2009) 365–395
Abstract

We show vanishing results about the infimum of the topological entropy of the geodesic flow of homogeneous smooth four-manifolds. We prove that any closed oriented geometric four-manifold has zero minimal entropy if and only if it has zero simplicial volume. We also show that if a four-manifold M admits a geometric decomposition in the sense of Thurston and does not have geometric pieces modelled on hyperbolic four-space 4, the complex hyperbolic plane 2 or the product of two hyperbolic planes 2 × 2 then M admits an –structure. It follows that M has zero minimal entropy and collapses with curvature bounded from below. We then analyse whether or not M admits a metric whose topological entropy coincides with the minimal entropy of M and provide new examples of manifolds for which the minimal entropy problem cannot be solved.

Keywords
minimal entropy, geodesic flows, geometric structures
Mathematical Subject Classification 2000
Primary: 37B40, 57M50
Secondary: 22F30, 53D25
References
Publication
Received: 21 April 2008
Revised: 5 February 2009
Accepted: 5 February 2009
Published: 25 February 2009
Authors
Pablo Suárez-Serrato
CIMAT
Jalisco S/N
Col. Valenciana
CP: 36240 Guanajuato, Gto
México.