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Dec 24, 2011 at 4:44 comment added Tom Church Every knot complement is an example of a 3-manifold with torus boundary (and there are tons more), so I am not sure that this example is so exciting.
Dec 24, 2011 at 4:38 history edited Chris Gerig CC BY-SA 3.0
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Dec 24, 2011 at 4:05 comment added Will Sawin However, note that neither is contractible.
Dec 24, 2011 at 3:55 history answered Chris Gerig CC BY-SA 3.0