Almost flat relative vector bundles and the almost monodromy correspondence

2019/08/28 by Kubota, Yosuke · 1 citation
#19K56 #55R50 #FOS: Mathematics #Geometric Topology (math.GT) #K-Theory and Homology (math.KT)

paper · doi:10.48550/arxiv.1908.10575

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.

Cited by

• On Chern classes of almost representations

Related

• The relative Mishchenko--Fomenko higher index and almost flat bundles II: Almost flat index pairing
• Almost flat bundles and homological invariance of infinite K-area
• Exotic smooth structures on topological fibre bundles I
• Definable structures on flat bundles
• Exotic smooth structures on topological fibre bundles II