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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).

4 votes

Introduction to Floer Theory?

I can vouch for Audin-Damian's Theorie de Morse et Homologie de Floer, read it cover to cover for my quals. They do Hamiltonian Floer theory with simplifying assumptions ($\omega$ and $c_1$ vanish on …