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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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Poincaré Conjecture and the Shape of the Universe

To me, one needs to look for an answer from the other end: Big Bang. If the Universe was born from a single 1-connected point and all the following expansion has no singularities, i.e. can be conside …
Nikolai Zaitsev's user avatar