http://www.openproblemgarden.org/op/what_is_the_homotopy_type_of_the_group_of_diffeomorphisms_of_the_4_sphere Comments for "What is the homotopy type of the group of diffeomorphisms of the 4-sphere?" en http://www.openproblemgarden.org/op/what_is_the_homotopy_type_of_the_group_of_diffeomorphisms_of_the_4_sphere <table cellspacing="10"> <tr> <td> Author(s): <a href="/category/smale_s">Smale</a>&nbsp;&nbsp; </td> <td align=right> Subject: <a href="/topology">Topology</a>&nbsp;&nbsp; </td> </tr> <tr> <td colspan=2> <table border=1 cellspacing="5"> <tr><td> <div class="envtheorem"><b>Problem</b>&nbsp;&nbsp; <img class="teximage" src="/files/tex/18446359b22efa9d172da85f2cb353a1171ad1d9.png" alt="$ Diff(S^4) $" /> has the homotopy-type of a product space <img class="teximage" src="/files/tex/ad3d9f988825524617e3f752930a949f55807846.png" alt="$ Diff(S^4) \simeq \mathbb O_5 \times Diff(D^4) $" /> where <img class="teximage" src="/files/tex/c7557ce04e95c8a9a974f0043bddb280c65324d3.png" alt="$ Diff(D^4) $" /> is the group of diffeomorphisms of the 4-ball which restrict to the identity on the boundary. Determine some (any?) homotopy or homology groups of <img class="teximage" src="/files/tex/c7557ce04e95c8a9a974f0043bddb280c65324d3.png" alt="$ Diff(D^4) $" />. </div> </tr></td> </table> </td> </tr> </table> Smale, S. 4-sphere diffeomorphisms Topology http://www.openproblemgarden.org/op/what_is_the_homotopy_type_of_the_group_of_diffeomorphisms_of_the_4_sphere#comment Sat, 07 Nov 2009 20:50:53 +0100 rybu 37159 at http://www.openproblemgarden.org