Volume 10, issue 1 (2006)

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Tightness and efficiency of irreducible automorphisms of handlebodies

Leonardo Navarro Carvalho

Geometry & Topology 10 (2006) 57–95

arXiv: math.GT/0408353


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.

automorphism, mapping class, handlebody, pseudo-Anosov, lamination, diffeomorphism
Mathematical Subject Classification 2000
Primary: 57M99
Secondary: 57N37
Forward citations
Received: 1 September 2004
Accepted: 26 November 2005
Published: 4 March 2006
Proposed: Cameron Gordon
Seconded: Dave Gabai, Jean-Pierre Otal
Leonardo Navarro Carvalho
Departamento de Matemática Aplicada
IM—Universidade Federal Fluminense
Niterói, RJ