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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).

8 votes
1 answer
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Outer automorphism group of Brieskorn homology sphere?

In this post, it is discussed how a Brieskorn homology sphere $\Sigma(a_1,a_2,a_3)$ with $\displaystyle \frac{1}{a_1}+ \frac{1}{a_2}+ \frac{1}{a_3} < 1$ is an aspherical manifold with a superperfect f …
0 votes

Torsion in homology or fundamental group of subsets of Euclidean 3-space

The answer in this post shows that if $U$ is open and connected, its fundamental group must be torsion-free.
Jeffrey Rolland's user avatar