Almost flat relative vector bundles and the almost monodromy correspondence
K-Theory and Homology
2019-08-29 v1 Geometric Topology
Abstract
In this paper we introduce the notion of almost flatness for (stably) relative bundles on a pair of topological spaces and investigate basic properties of it. First, we show that almost flatness of topological and smooth sense are equivalent. This provides a construction of an almost flat stably relative bundle by using the enlargeability of manifolds. Second, we show the almost monodromy correspondence, that is, a correspondence between almost flat (stably) relative bundles and (stably) relative quasi-representations of the fundamental group.
Keywords
Cite
@article{arxiv.1908.10575,
title = {Almost flat relative vector bundles and the almost monodromy correspondence},
author = {Yosuke Kubota},
journal= {arXiv preprint arXiv:1908.10575},
year = {2019}
}
Comments
25 pages, separated from Section 5, 6.2 of arXiv:1807.03181, corrected minor errors