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the question is already clear from the title, but I have to add at least 30 useless characters.

The question is equivalent to ask if the normal bundle of the boundary is stably trivial

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1) Did you mean "The question is already clear..."?$$ $$2) The question should be readable without the title. –  Rasmus Jan 31 '13 at 17:28
3) you could have used the 30 useless characters to add a few words, like why you think this is true, what you know about bundles over a contractible manifold, etc. –  Martin Jan 31 '13 at 17:32
OPS! yes! thankyou! –  fritz Jan 31 '13 at 17:32
and the normal bundle is trivial, no?(Fix a metric, and take the unit outward vector field) –  user27126 Jan 31 '13 at 18:04

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