Timeline for Torsion elements in the mapping class group
Current License: CC BY-SA 3.0
10 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 12, 2016 at 13:36 | answer | added | Sam Nead | timeline score: 6 | |
| Feb 23, 2015 at 6:42 | comment | added | ThiKu | The latter classifies orientation-preserving actions of finite groups in genus 2 and 3: sciencedirect.com/science/article/pii/002240499190021S# | |
| Feb 23, 2015 at 5:51 | comment | added | ThiKu | There is a book by Zieschang "Finite groups of mapping classes of surfaces" Which basically reflects the state of the Art before Kerckhoff's proof of Nielsen realization. For the latter see Kerckhoff's "The Nielsen realization problem". (There is an announcements in BAMS and the paper in the Annals.) Another account is Broughton: "Classifying finite group actions on surfaces of low genus". | |
| Feb 22, 2015 at 21:51 | comment | added | HJRW | Possibly what the OP want for question 1 is Nielsen realization? | |
| Feb 22, 2015 at 19:30 | comment | added | Ryan Budney | It seems all your questions have been answered in the comments. It's not so clear what you mean by your question (1) -- torsion elements appear to be able to do pretty much anything. If you need examples to help you think through these types of questions, there's a pencil-and-paper technique to enumerate through the conjugacy classes of finite-order elements of the mapping class group (even allowing orientation-reversing automorphisms). It's the classification of Seifert-fibred 3-manifolds, restricted to the class that fibre over $S^1$. | |
| Feb 22, 2015 at 19:08 | comment | added | Alex Degtyarev | Sorry, what I mean is that you can take any closed surface and any finite group acting on it, and remove disks about any orbit of this group. So, examples are a plenty. | |
| Feb 22, 2015 at 19:05 | comment | added | Alex Degtyarev | Why not? Say, two boundary components permuted? Or even one boundary component "about" one fixed point? | |
| Feb 22, 2015 at 19:03 | comment | added | Anonymous | hyperelliptic involutions on surfaces with boundary? | |
| Feb 22, 2015 at 19:02 | comment | added | Alex Degtyarev | 2 and 3 are certainly wrong, examples being a plenty (e.g., hyperelliptic involutions). Maybe, not on any surface, though. | |
| Feb 22, 2015 at 19:00 | history | asked | Anonymous | CC BY-SA 3.0 |