Combinatorial Group Theory: COMBINATORIAL GROUP THEORY

The topology of Stein surfaces and contact 3-manifolds is studied by means of handle decompositions. A simple characterization of homeomorphism types of Stein surfaces is obtained-they correspond to open handlebodies with all handles of index < 2. An uncountable collection of exotic l4,'S is shown to admit Stein structures. New invariants of contact 3-manifolds are produced, including a complete (and computable) set of invariants for determining the homotopy class of a 2-plane field on a 3-manifold. These invariants are applicable to Seiberg-Witten theory. Several families of oriented 3-manifolds are examined, namely the Seifert fibered spaces and all surgeries on various links in S3, and in each case it is seen that "most" members of the family are the

Handlebody construction of Stein surfaces

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Metric Spaces Of Non Positive Curvature

We summarize properties of 3-manifold groups, with a particular focus on the consequences of the recent results of Ian Agol, Jeremy Kahn, Vladimir Markovic and Dani Wise.

3-Manifold Groups

On Seifert-manifolds

Essential laminations in seifert-fibered spaces

http://www.math.unl.edu/~mbrittenham2/papers/pdf/subgroups.free.ig.semigroups.pdf

Subgroups of free idempotent generated semigroups need not be free

We will classify all exceptional Dehn surgeries on 2-bridge knots according to whether they produce reducible, toroidal, or small Seifert fibered manifolds.

The classification of exceptional Dehn surgeries on 2-bridge knots

We use topological methods to study the maximal subgroups of the free idempotent generated semigroup on a biordered set. We use these to give an example of a free idempotent generated semigroup with maximal subgroup isomorphic to the free abelian group of rank 2. This is the first example of a non-free subgroup of a free idempotent generated semigroup.

We examine the existence of foliations without Reeb components, taut foliations, and foliations with no S S-leaves, among graph manifolds. We show that each condition is strictly stronger than its predecessor(s), in the strongest possible sense; there are manifolds admitting foliations of each type which do not admit foliations of the succeeding type(s).

/pdf/graph-manifolds-and-taut-foliations-iao5pwhogt.pdf

Mark Brittenham

Papers

Essential laminations in seifert-fibered spaces

Subgroups of free idempotent generated semigroups need not be free

The classification of exceptional Dehn surgeries on 2-bridge knots

Subgroups of free idempotent generated semigroups need not be free

Graph manifolds and taut foliations