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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).

2 votes

Proof of the Reidemeister theorem

If you are willing to take a difficult theorem of Moise for granted (which proves equivalence of link isotopy in the smooth (tame) and PL category, in his "Affine Structures in 3 Manifolds VIII"), the …
Reza Rezazadegan's user avatar
11 votes

Maslov index and Heegard Floer homology

Knowing that the maslov index is equal to the "expected" dimension of the moduli space of the disks is helpful too. For example in the figure on the right side of page 17, you can see that a holomorph …
Reza Rezazadegan's user avatar