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
Geometric Topology, Low dimensional topology, Deformation theory
Geometric topology, L2 topological invariants.
- Geometric topology of manifolds of dimension > 3
- Group actions by homeomorphisms on manifolds
- Computations in algebraic K-theory and L-theory
Algorithmic questions in 3-manifold topology
Kevin P. Scannell
Hyperbolic 3-manifolds, spaces of knots
Geometric topology, Knot Theory
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.