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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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Compact contractible topological manifold with boundary=sphere is a ball

(this question is joint with Steven Karp and Thomas Lam) We need to use the following fact in our paper: Theorem 1. Let $M^n$ be a compact contractible topological manifold with boundary, such tha …
Pavel Galashin's user avatar