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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).

1 vote

Trigonal loci in Teichmueller spaces

The trigonal locus in the Teichmuller space - under mild hypotesis - is connected. The answer follows from one of the main results of http://arxiv.org/abs/1403.7399
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6 votes

Do mapping classes have gonality?

it seems that your question about the possible surjectivity of the map $$\pi_1(T_g) \to \pi_1(M_g)$$ has been recently answered positively in http://arxiv.org/abs/1403.7399 (see the very first page …
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