Tangential homotopy equivalences (Ex)
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Diarmuid Crowley (Talk | contribs)
(Created page with "<wikitex>; A homotopy equivalence $f \colon M \to N$ of closed smooth $n$-manifolds is called ''tangential'' if $f^*TN \cong TM$; i.e. $f$ pulls back the tangent bundle of $N$...")
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(Created page with "<wikitex>; A homotopy equivalence $f \colon M \to N$ of closed smooth $n$-manifolds is called ''tangential'' if $f^*TN \cong TM$; i.e. $f$ pulls back the tangent bundle of $N$...")
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Revision as of 23:50, 25 August 2013
A homotopy equivalence of closed smooth -manifolds is called tangential if ; i.e. pulls back the tangent bundle of to .
Example 0.1.
- Given an example of a tangential homotopy equivalence which is not homotopic to a diffeomorphism.
- Show that if is a tangential homotopy equivelance, then there is a diffeomorphism