Volume 9, issue 1 (2009)

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

Volume 16
Issue 4, 1827–2458
Issue 3, 1253–1825
Issue 2, 621–1251
Issue 1, 1–620

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
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

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.

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