smooth homotopy on exotic R^4 - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-19T12:07:00Z http://mathoverflow.net/feeds/question/103586 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/103586/smooth-homotopy-on-exotic-r4 smooth homotopy on exotic R^4 Maciej Starostka 2012-07-31T07:48:15Z 2012-07-31T11:01:38Z <p>Take an exotic $\mathbb{R}^4$ i.e. $V = (\mathbb{R}^4,d)$ such that $V$ is not diffeomorphic to $\mathbb{R}^4$ with standard metric.</p> <p>Is it true (obvious?) that any two smooth maps $f_1, f_2: S^k \to V$ are equivalent via <strong>smooth</strong> homotopy?</p> <p>edited: (for any k)</p> http://mathoverflow.net/questions/103586/smooth-homotopy-on-exotic-r4/103589#103589 Answer by Mark Grant for smooth homotopy on exotic R^4 Mark Grant 2012-07-31T08:14:30Z 2012-07-31T11:01:38Z <p>Yes, since smooth maps which are (continuously) homotopic are always smoothly homotopic. See Kosinski's "Differential Manifolds", Theorem III.2.5 and Corollary III.2.6.</p>