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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

a question on rank of fundamental group

Complementing Misha's answer, the following is true for any non-(virtually cyclic) hyperbolic group $G$: Claim: for any sufficiently large $k \in \mathbb{N}$ there is a free quasiconvex subgroup $H_ …
Ashot Minasyan's user avatar
5 votes
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Solving equations in hyperbolic groups and subgroups of isometry of a Gromov hyperbolic space

The statement about the hyperbolic group $\Gamma$ is true if $\Gamma$ is torsion-free. This follows from work on special elements in hyperbolic (and relatively) hyperbolic groups. In the torsion-free …
Ashot Minasyan's user avatar