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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).

16 votes
2 answers
754 views

Can a sphere glued into a soft 3d-mattress rotate continuously? (manifolds, SU(2) and the be...

The question is triggered by the wonderful animations by Jason Hise: https://www.youtube.com/watch?v=LLw3BaliDUQ https://www.youtube.com/watch?v=6Ul_-ABYaYU https://www.youtube.com/watch?v=aYVt1U …