Mapping class groups of medium distance Heegaard splittings
نویسندگان
چکیده
منابع مشابه
Mapping Class Groups of Heegaard Splittings
The mapping class group of a Heegaard splitting is the group of connected components in the set of automorphisms of the ambient manifold that map the Heegaard surface onto itself. We find examples of elements of the mapping class group that are periodic, reducible and pseudo Anosov on the Heegaard surface, but are isotopy trivial in the ambient manifold. We prove structural theorems about the f...
متن کاملDistance of Heegaard Splittings of Knot Complements
Let K be a knot in a closed orientable irreducible 3-manifold M and let P be a Heegaard splitting of the knot complement of genus at least two. Suppose Q is a bridge surface for K. Then either • d(P ) ≤ 2 − χ(Q −K), or • K can be isotoped to be disjoint from Q so that after the isotopy Q is a Heegaard surface for the knot exterior that is isotopic to a possibly stabilized copy of P .
متن کاملBig Heegaard Distance Implies Finite Mapping Class Group
We show that if M is a closed three manifold with a Heegaard splitting with sufficiently big Heegaard distance then the subgroup of the mapping class group of the Heegaard surface, whose elements extend to both handlebodies is finite. As a corollary, this implies that under the same hypothesis, the mapping class group of M is finite.
متن کاملSaddle Tangencies and the Distance of Heegaard Splittings
We give another proof of a theorem of Scharlemann and Tomova and of a theorem of Hartshorn. The two theorems together say the following. Let M be a compact orientable irreducible 3–manifold and P a Heegaard surface of M . Suppose Q is either an incompressible surface or a strongly irreducible Heegaard surface in M . Then either P ∩ Q = ∅ after an isotopy or the Hempel distance d(P ) ≤ 2genus(Q)...
متن کاملDistances of Heegaard splittings
J Hempel [Topology, 2001] showed that the set of distances of the Heegaard splittings (S,V, h(V)) is unbounded, as long as the stable and unstable laminations of h avoid the closure of V ⊂ PML(S). Here h is a pseudo-Anosov homeomorphism of a surface S while V is the set of isotopy classes of simple closed curves in S bounding essential disks in a fixed handlebody. With the same hypothesis we sh...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 2010
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-2010-10545-2