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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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Hopf reference sought

For a vector $w$, let $T_{w}$ be the translation by $w$. I was told that the following observation about subsets of the plane was due to H. Hopf: Let $X$ be a compact, path-connected subset of the p …
Andrew Clifford's user avatar