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Topology

Saint Louis University has a very active research group in topology,with an emphasis on the topology of 3-dimensional manifolds. Areas of specialty include hyperbolic 3-manifolds, hyperbolic geometry, knot theory and foliations.

People specializing in this area

Faculty

Anneke Bart

Geometric Topology, Low dimensional topology, Deformation theory

John Cantwell

Foliations

Bryan Clair

Geometric topology, L2 topological invariants.

Qayum Khan

  • Geometric topology of manifolds of dimension > 3
  • Group actions by homeomorphisms on manifolds
  • Computations in algebraic K-theory and L-theory

David Letscher

Algorithmic questions in 3-manifold topology

Kevin P. Scannell

Hyperbolic 3-manifolds, spaces of knots

Christine Stevens

Topological groups.

Michael Tsau

Geometric topology, Knot Theory

Graduate Students

Gerrit Smith

Stable Geometric Topology of 4-Manifolds

Geometric topology of smooth 4-manifolds up to stablization with S2xS2

Consider a separating 3-dimensional submanifold of a smooth 4-dimensional manifold whose fundamental group is mapped injectively into the fundamental group of the 4-manifold. The Seifert–van Kampen theorem implies the fundamental group of the 4-manifold has an amalgamated product structure.  This work attempts to characterize when the converse holds, allowing for stabilization of the 4-manifold by forming the connected sum with S2xS2 factors.  When such decompositions can be realized geometrically, uniqueness of the decomposition is characterized.

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