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Homotopy theory, homological algebra, algebraic treatments of manifolds.
6
votes
Functoriality of Thurston's norm
For submanifolds that are link complements, Ken Baker and I recently investigated this question in our paper "Dehn Filling and the Thurston Norm" available at arXiv:1608.02443
The basic idea (as in so …
2
votes
3-manifolds homotopy equivalent to a surface
This paper gives some other very nice counter-examples. As I recall, for open manifolds you really need to think about proper homotopies, not just homotopies.
MR1033220 (91b:57021) Reviewed
Scott, P …
5
votes
Knot theory in handlebodies of arbitrary genus
If you mean adding 1 and 2 handles to the boundary of the ball, that will never change the (non)triviality of the knot in the 3-ball. On the other hand, perhaps the notion of tunnel number is what you …