Manifolds cross a circle (Ex)
From Manifold Atlas
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(Created page with "<wikitex>; Suppose that $M$ and $N$ are closed smooth simply-connected manifolds and that there is a diffeomorphism $$ f \colon M \times S^1 \cong N \times S^1.$$ Show that $M...") |
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| − | Suppose that $M$ and $N$ are closed smooth simply-connected manifolds and that there is a diffeomorphism | + | Suppose that $M$ and $N$ are closed smooth simply-connected $n$-manifolds, $n \geq 5$, and that there is a diffeomorphism |
$$ f \colon M \times S^1 \cong N \times S^1.$$ | $$ f \colon M \times S^1 \cong N \times S^1.$$ | ||
Show that $M$ and $N$ are diffeomorphic. | Show that $M$ and $N$ are diffeomorphic. | ||
Latest revision as of 23:10, 25 August 2013
Suppose that 
and 
are closed smooth simply-connected 
-manifolds, 
, and that there is a diffeomorphism
Show that and are diffeomorphic.
If and are not simply-connected, what condition would you place on the fundamental group to
obtain a similar theoroem?
