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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).

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What is a finite Haken cover of the Seifert–Weber space?

It's known that the Seifert–Weber space (obtained from a dodecahedron by gluing opposite faces with a 3/10 turn) is an example of a non-Haken 3-manifold. Since every closed 3-manifold is virtually Hak …
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