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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

Is the topological concept of collapsible useful?

A small addendum: Collapses seem also useful in some applications, namely practical homology computations, as preprocessing steps for algorithms that compute homology. (Concretely - say you have to co …
Bruno Benedetti's user avatar
10 votes
1 answer
419 views

Heegaard genus of the hyperbolic dodecahedral space (is it 3 or 4?)

I have a question on the hyperbolic dodecahedral space, first described by C.Weber and H. Seifert in 1933 [Die beiden Dodekaederr\"aume, Math Z. 37 (1933), 237-253]. Is it known whether it admits a He …
Bruno Benedetti's user avatar