Timeline for Diffeomorphism coming from the s-cobordism theorem

8 events

when toggle format	what		by	license	comment
Dec 21, 2012 at 19:07	vote	accept	Mauricio
Dec 21, 2012 at 19:07	vote	accept	Mauricio
Dec 21, 2012 at 19:07
Dec 21, 2012 at 17:50	comment	added	Misha		@Mauricio: No, the answer is nontrivial for maps homotopic to the identity, see my comment above. (That is, unless you regard, say, existence of exotic spheres and Cerf's theory as trivialities. :-))
Dec 21, 2012 at 16:41	comment	added	Mauricio		@Tom Goodwillie: If one adds the condition that $f$ is homotopic to the identity, is the answer pretty trivially no again?...
Dec 21, 2012 at 16:19	vote	accept	Mauricio
Dec 21, 2012 at 16:23
Dec 21, 2012 at 15:36	vote	accept	Mauricio
Dec 21, 2012 at 16:18
Dec 21, 2012 at 6:37	comment	added	Misha		Tom: The question is, indeed, poorly phrased. I think, OP is asking for conditions under which a diffeomorphism $f: M\to M$ is (smoothly) pseudo-isotopic to the identity. The obvious necessary condition, as you observed, is that $f$ is homotopic to the identity. There are diffeomorphisms of $S^6$ which are homotopic but not (smoothly) pseudo-isotopic to the identity (coming from exotic 7-spheres). If $M$ is simply-connected (of dimension $\ge 5$) then Cerf proved that smooth pseudo-isotopy is equivalent to smooth isotopy, which is the best one can hope for.
Dec 21, 2012 at 1:47	history	answered	Tom Goodwillie	CC BY-SA 3.0