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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).

17 votes
3 answers
2k views

Is it true that all sphere bundles are boundaries of disk bundles?

Let $E$ be the total space of the sphere bundle $S^k\to E\to M$, is it true that there exists a disk bundle $D^{k+1}\to N\to M$ such that $E=\partial N$? (where $D^{k+1}$ is the unit disk in $\mathbb …
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2 votes
2 answers
376 views

Any introduction to Teichmuller Space of $T^2$?

Is there any well written introduction for the modular space of complex structures on $T^2$?