Configured locally smooth cohomology and $\mathbb{Q}/\mathbb{Z}$-torsion in $H_3$ of diffeomorphism groups
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866912817694638080 |
|---|---|
| author | Nosaka, Takefumi |
| author_facet | Nosaka, Takefumi |
| contents | We introduce configured group cohomology, a variant of locally smooth cohomology built from well-configured tuples and geometric fillings. This framework yields explicit locally smooth $\R/\Z$-valued $3$-cocycles of Chern--Simons type on diffeomorphism groups preserving geometric structures. As an application we show that, for several such groups, the third group homology contains a subgroup isomorphic to $\Q/\Z$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_07230 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Configured locally smooth cohomology and $\mathbb{Q}/\mathbb{Z}$-torsion in $H_3$ of diffeomorphism groups Nosaka, Takefumi Geometric Topology Algebraic Topology 57M50, 57S05, 58D05, 22E65, 20J06 We introduce configured group cohomology, a variant of locally smooth cohomology built from well-configured tuples and geometric fillings. This framework yields explicit locally smooth $\R/\Z$-valued $3$-cocycles of Chern--Simons type on diffeomorphism groups preserving geometric structures. As an application we show that, for several such groups, the third group homology contains a subgroup isomorphic to $\Q/\Z$. |
| title | Configured locally smooth cohomology and $\mathbb{Q}/\mathbb{Z}$-torsion in $H_3$ of diffeomorphism groups |
| topic | Geometric Topology Algebraic Topology 57M50, 57S05, 58D05, 22E65, 20J06 |
| url | https://arxiv.org/abs/2601.07230 |