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Mar 27, 2010 at 18:46 vote accept Sergei Ivanov
Mar 27, 2010 at 16:54 answer added Anton Petrunin timeline score: 3
Mar 19, 2010 at 23:38 history edited Sergei Ivanov CC BY-SA 2.5
noticed that the first question is answered
Mar 19, 2010 at 23:25 comment added Ryan Budney If the boundary is a standard sphere then the contractible manifold has to be the standard disc. This is an h-cobordism theorem type argument -- puncture your contractible manifold, this gives an h-cobordism, etc.
Mar 19, 2010 at 23:21 comment added Sergei Ivanov I see. By the way, are there examples bounded by the standard sphere?
Mar 19, 2010 at 22:51 history edited Sergei Ivanov CC BY-SA 2.5
added a remark about distance function
Mar 19, 2010 at 22:43 answer added Igor Belegradek timeline score: 6
Mar 19, 2010 at 22:42 comment added Ryan Budney No. See the Wikipedia page on Mazur manifolds for examples and relevant history of your question.
Mar 19, 2010 at 22:32 answer added Petya timeline score: 7
Mar 19, 2010 at 22:03 history asked Sergei Ivanov CC BY-SA 2.5