Timeline for Mapping class group and surgery theory
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 20, 2021 at 12:11 | comment | added | ThorbenK | I don't know how related this is to what you had in mind, but Kreck established something rougly called "bordisms of diffeomorphisms" and these are closely related to mapping tori (i.e. taking $M\times [0,1]$ and gluing the ends together via your diffeomorphism) | |
| Oct 4, 2021 at 21:47 | comment | added | Connor Malin | Sorry, I meant to include it: "A geometric formulation of surgery". It is difficult to read in my opinion, so I might recommend reading the intro to section 2 of arxiv.org/pdf/2002.04647.pdf . The point being that Quinn's structure space $S(M)$ can be written as a quotient of homotopy automorphisms modulo block diffeomorphisms, both of which are easier to study than $\operatorname{Diff}(M)$ with homotopy theory. | |
| Oct 4, 2021 at 20:56 | comment | added | Student | Which paper of Quinn did you mean? | |
| Oct 4, 2021 at 17:40 | comment | added | Connor Malin | Your cobordism is always diffeomorphic to the trivial cobordism by sending $(x,t)$ to $(x,t/2)$ if $t \leq 1$ and to $(\phi^{-1}(x),t/2)$ if $t \geq 1$. You are not wrong to say there is a connection though between surgery theory and mapping class groups, though I think it is much easier to study the components of $\operatorname{Diff(M)}$ with it than the actual mapping class group. Quinn formulated this approach in his paper on surgery spaces. | |
| Oct 3, 2021 at 14:51 | history | asked | Student | CC BY-SA 4.0 |