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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).

7 votes

Reference for topological graph theory (research / problem-oriented)

I can recommend Topics in Chromatic Graph Theory (Encyclopedia of Mathematics and its Applications) with editors Lowell W. Beineke and Robin J. Wilson. It is from 2015, and if you are interested in ch …