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Topology of cell complexes and manifolds, classification of manifolds (e.g. smoothing, surgery), low dimensional topology (e.g. knot theory, invariants of 4-manifolds), embedding theory, combinatorial and PL topology, geometric group theory, infinite dimensional topology (e.g. Hilbert cube manifolds, theory of retracts).

12 votes
1 answer
296 views

Hyperbolic 3-manifold groups acting on the plane

Can the fundamental group of a closed hyperbolic 3-manifold act freely on the plane by homeomorphisms? Freely and cocompactly? Freely, cocompactly, and preserving orientation?
Steven Frankel's user avatar
6 votes

What (if anything) happened to Intersection Homology?

There do seem to be people thinking about it. I heard Sylvain Cappell lecture a few weeks ago; he spoke about using intersection (co)homology as part of a generalization of characteristic classes to s …
Steven Frankel's user avatar