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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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Homotopy Extension Property (HEP)
I want to show (although Artin gave an ad hoc proof) that if two braids \beta and \beta' are isotopic as braids, then they are equivalent as tangles. I'd like to use the homotopy extension property ( …