Tightness and efficiency of irreducible automorphisms of handlebodies

Carvalho, Leonardo Navarro

doi:10.2140/gt.2006.10.57

Download this article
	For screen
	For printing

Recent Issues

The Journal

Submission Guidelines

Submission Page

Policies for Authors

Ethics Statement

ISSN 1364-0380 (online)

ISSN 1465-3060 (print)

Author Index

To Appear

Other MSP Journals

Tightness and efficiency of irreducible automorphisms of handlebodies

Leonardo Navarro Carvalho

Geometry & Topology 10 (2006) 57–95

DOI: 10.2140/gt.2006.10.57

arXiv: math.GT/0408353

Abstract

Among (isotopy classes of) automorphisms of handlebodies those called irreducible (or generic) are the most interesting, analogues of pseudo-Anosov automorphisms of surfaces. We consider the problem of isotoping an irreducible automorphism so that it is most efficient (has minimal growth rate) in its isotopy class. We describe a property, called tightness, of certain invariant laminations, which we conjecture characterizes this efficiency. We obtain partial results towards proving the conjecture. For example, we prove it for genus two handlebodies. We also show that tightness always implies efficiency.

In addition, partly in order to provide counterexamples in our study of properties of invariant laminations, we develop a method for generating a class of irreducible automorphisms of handlebodies.

Keywords

automorphism, mapping class, handlebody, pseudo-Anosov, lamination, diffeomorphism

Mathematical Subject Classification 2000

Primary: 57M99

Secondary: 57N37

References

Forward citations

Publication

Received: 1 September 2004

Accepted: 26 November 2005

Published: 4 March 2006

Proposed: Cameron Gordon

Seconded: Dave Gabai, Jean-Pierre Otal

Authors

Leonardo Navarro Carvalho
Departamento de Matemática Aplicada IM—Universidade Federal Fluminense Niterói, RJ Brazil

Volume 10, issue 1 (2006)