On flat manifold bundles and the connectivity of Haefliger's classifying spaces

Sam Nariman

On flat manifold bundles and the connectivity of Haefliger's classifying spaces

Geometric Topology 2024-05-17 v3 Algebraic Topology Group Theory

Authors: Sam Nariman

Abstract

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.

Keywords

flat manifold bundles haefliger classifying space foliated bundles haefliger-thurston conjecture bordism holonomy

Cite

@article{arxiv.2202.00052,
  title  = {On flat manifold bundles and the connectivity of Haefliger's classifying spaces},
  author = {Sam Nariman},
  journal= {arXiv preprint arXiv:2202.00052},
  year   = {2024}
}

Comments

This version is to appear in the Proceedings of the AMS

On flat manifold bundles and the connectivity of Haefliger's classifying spaces

Abstract

Keywords

Cite

Comments

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