Examples of Irreducible Automorphisms of Handlebodies
نویسنده
چکیده
Automorphisms of handlebodies arise naturally in the classification of automorphisms of three-manifolds. Among automorphisms of handlebodies, there are certain automorphisms called irreducible (or generic), which are analogues of pseudo-Anosov automorphisms of surfaces. We show that irreducible automorphisms of handlebodies exist and develop methods for constructing a range of examples.
منابع مشابه
Tightness and efficiency of irreducible automorphisms of handlebodies
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, whic...
متن کاملAutomorphisms of 3-Dimensional Handlebodies
This paper gives a classification up to isotopy of automorphisms (self-homeomorphisms) of 3-dimensional handlebodies and compression bodies, analogous to the Nielsen-Thurston classification of automorphisms of surfaces. Indecomposable automorphisms analogous to pseudo-Anosov automorphisms are identified and called generic. The first steps are taken towards understanding generic automorphisms us...
متن کاملReal Theta Characteristics and Automorphisms of a Real Curve
Let X be a geometrically irreducible smooth projective curve, defined over R, of genus at least two that admits nontrivial automorphisms. Fix a nontrivial automorphism σ of X. Assume that X does not have any real points. Then σ acts trivially on the set of all real theta characteristics of X if and only if X is hyperelliptic with σ being the unique hyperelliptic involution of X. Examples are gi...
متن کاملLocal Rigidity for Anosov Automorphisms
We consider an irreducible Anosov automorphism L of a torus Td such that no three eigenvalues have the same modulus. We show that L is locally rigid, that is, L is C1+Hölder conjugate to any C1-small perturbation f such that the derivative Dpf is conjugate to Ln whenever fnp = p. We also prove that toral automorphisms satisfying these assumptions are generic in SL(d,Z). Examples constructed in ...
متن کاملLocally unknotted spines of Heegaard splittings
We show that under reasonable conditions, the spines of the handlebodies of a strongly irreducible Heegaard splitting will intersect a closed ball in a graph which is isotopic into the boundary of the ball. This is in some sense a generalization of the results by Scharlemann on how a strongly irreducible Heegaard splitting surface can intersect a ball. AMS Classification 57M27; 57Q10
متن کامل