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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).
14
votes
Accepted
Information about Milnor conjecture
According to David Roberts comment and the following paper it is open for dimensions $n\geq 4$.
Pan, Jiayin, A proof of Milnor conjecture in dimension 3, J. Reine Angew. Math. 758, 253-260 (2020). ZBL …
3
votes
De Rham decomposition theorem, generalisations and good references
Response to the first question:
Pantilie, Radu, A simple proof of the de Rham decomposition theorem, Bull. Math. Soc. Sci. Math. Roum., Nouv. Sér. 36, No. 3-4, 341-343 (1992). ZBL0811.53040.