On flat manifold bundles and the connectivity of Haefliger's classifying spaces
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2022
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866929344386957312 |
|---|---|
| author | Nariman, Sam |
| author_facet | Nariman, Sam |
| contents | We investigate a conjecture due to Haefliger and Thurston in the context of foliated manifold bundles. In this context, Haefliger-Thurston's conjecture predicts that every $M$-bundle over a manifold $B$ where $\text{dim}(B)\leq \text{dim}(M)$ is cobordant to a flat $M$-bundle. In particular, we study the bordism class of flat $M$-bundles over low dimensional manifolds, comparing a finite dimensional Lie group $G$ with $\text{Diff}_0(G)$ and localizing the holonomy of flat M-bundles to be supported in a ball. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2202_00052 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | On flat manifold bundles and the connectivity of Haefliger's classifying spaces Nariman, Sam Geometric Topology Algebraic Topology Group Theory 57R50, 57R32, 57R52, 57R65, 57R40, 57R19, 53D10, 58D05, 57Q35 We investigate a conjecture due to Haefliger and Thurston in the context of foliated manifold bundles. In this context, Haefliger-Thurston's conjecture predicts that every $M$-bundle over a manifold $B$ where $\text{dim}(B)\leq \text{dim}(M)$ is cobordant to a flat $M$-bundle. In particular, we study the bordism class of flat $M$-bundles over low dimensional manifolds, comparing a finite dimensional Lie group $G$ with $\text{Diff}_0(G)$ and localizing the holonomy of flat M-bundles to be supported in a ball. |
| title | On flat manifold bundles and the connectivity of Haefliger's classifying spaces |
| topic | Geometric Topology Algebraic Topology Group Theory 57R50, 57R32, 57R52, 57R65, 57R40, 57R19, 53D10, 58D05, 57Q35 |
| url | https://arxiv.org/abs/2202.00052 |