2023/02/06 by Chen, Xujia
#57N16 #57R20 #FOS: Mathematics #Geometric Topology (math.GT)
paper · doi:10.48550/arxiv.2302.03021
Kontsevich's characteristic classes are invariants of framed smooth fiber bundles with homology sphere fibers. It was shown by Watanabe that they can be used to distinguish smooth S4-bundles that are all trivial as topological fiber bundles. In this article we show that this ability of Kontsevich's classes is a manifestation of the following principle: the ``real blow-up'' construction on a smooth manifold essentially depends on its smooth structure and thus, given a smooth manifold (or smooth fiber bundle) M, the topological invariants of spaces constructed from M by real blow-ups could potentially differentiate smooth structures on M. The main theorem says that Kontsevich's characteristic classes of a smooth framed bundle π are determined by the topology of the 2-point configuration space bundle of π and framing data.