| Title:
|
Disordered arcs and Harer stability (English) |
| Author:
|
Wahl, Nathalie |
| Author:
|
Harr, Oscar |
| Author:
|
Vistrup, Max |
| Language:
|
English |
| Journal:
|
Higher Structures |
| ISSN:
|
2209-0606 |
| Volume:
|
8 |
| Issue:
|
1 |
| Year:
|
2024 |
| Pages:
|
193-223 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We give a new proof of homological stability with the best known isomorphism range for mapping class groups of surfaces with respect to genus. The proof uses the framework of Randal-Williams–Wahl and Krannich applied to disk stabilization in the category of bidecorated surfaces, using the Euler characteristic instead of the genus as a grading. The monoidal category of bidecorated surfaces does not admit a braiding, distinguishing it from previously known settings for homological stability. Nevertheless, we find that it admits a suitable Yang–Baxter element, which we show is sufficient structure for homological stability arguments. (English) |
| Keyword:
|
Homological stability |
| Keyword:
|
mapping class groups |
| MSC:
|
57M07 |
| MSC:
|
57R50 |
| idZBL:
|
Zbl 1571.57072 |
| idMR:
|
MR4752520 |
| DOI:
|
10.21136/HS.2024.04 |
| . |
| Date available:
|
2026-03-13T14:07:49Z |
| Last updated:
|
2026-03-13 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/153468 |
| . |
| Reference:
|
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