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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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The action of torsion of $MCG(S)$ on curve complex

Here is an example which can be easily generalized for all $S_g$, $g\geq 3$. With similar approaches, one can construct many examples, not just starting with the building block $S_{1,2}$. Notice the D …
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