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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 …
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 …