Essential disks and semi-essential surfaces in 3-manifolds

Details Essential disks and semi-essential surfaces in 3-manifolds Essential disks and semi-essential surfaces in 3-manifolds

2010-05-05

arxiv.org/abs/1005.0680v1

Mathematics

Geometric Topology

17 pages

Scientific paper

If M is a manifold with compressible boundary, we analyze essential disks in M, as well as incompressible, but not necessarily boundary incompressible, surfaces in M. We are most interested in the case where M is a handlebody or compression body. The analysis depends on a new normal surface theory. We hope the normal surface theory will be used in other papers to describe objects representing limits of essential disks in a handlebody or a 3-manifold with compressible boundary. For certain automorphisms of handlebodies, these disk limits should serve as invariant objects akin to laminations and analogous to the invariant laminations for pseudo-Anosov automorphisms of surfaces.

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