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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).

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Bloch group, hyperbolic manifolds and rigidity

In answer to question 3 it is not possible to go from an element of the Bloch group to a hyperbolic manifold as there are different three manifolds with the same element in the Bloch group. That is di …
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