Timeline for Equivariant handle decompositions
Current License: CC BY-SA 3.0
9 events
| when toggle format | what | by | license | comment | |
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| Apr 12, 2018 at 17:58 | comment | added | Chris Schommer-Pries | When $M=S^n$ is a sphere, then the space of orientation preserving homeomorphism is arc connected. In this case $G \to \textrm{Homeo}^+(M)/\textrm{homotopy} = pt$ seems to be no data at all? Is that really what you mean? | |
| Apr 12, 2018 at 17:09 | comment | added | Tim Campion | @JohnPardon do you mean "two maps of $Homeo(M)$ are equivalent iff they are homotopic through homeomorphisms as maps $M \to M$? Because otherwise it's not clear that the inverses of equivalent maps are equivalent. | |
| Apr 12, 2018 at 16:51 | history | bumped | CommunityBot | This question has answers that may be good or bad; the system has marked it active so that they can be reviewed. | |
| Mar 13, 2018 at 15:54 | history | bumped | CommunityBot | This question has answers that may be good or bad; the system has marked it active so that they can be reviewed. | |
| Aug 9, 2012 at 15:45 | comment | added | John Pardon | Say that two elements of $\operatorname{Homeo}(M)$ are equivalent iff they are homotopic as maps $M\to M$. This is an equivalence relation, and the group operation on $\operatorname{Homeo}(M)$ descends to the quotient. | |
| Aug 9, 2012 at 13:40 | comment | added | John Klein | Can you be more precise about the meaning of "$G\to\operatorname{Homeo}(M)/\text{homotopy}.$" ? | |
| Aug 9, 2012 at 13:27 | answer | added | Allan Edmonds | timeline score: 4 | |
| Aug 9, 2012 at 3:15 | comment | added | Andy Putman | This does not answer your question, but provides a different approach to the Morse theory in the first part. A theorem of Illman says that if $M$ is a manifold and $G$ is a finite group acting on $M$, then $M$ has a $G$-invariant triangulation. You could get an equivariant handle decomposition from this, but it is in some sense more rigid. See MR1770606 (2001j:57032) Illman, Sören(FIN-HELS) Existence and uniqueness of equivariant triangulations of smooth proper G-manifolds with some applications to equivariant Whitehead torsion. J. Reine Angew. Math. 524 (2000), 129–183. | |
| Aug 9, 2012 at 2:52 | history | asked | John Pardon | CC BY-SA 3.0 |