Kontsevich's characteristic classes as topological invariants of configuration space bundles

Chen X. Kontsevich’s characteristic classes as topological invariants of configuration space bundles. arXiv, 2302.03021.

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Abstract
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 $S^4$-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.
Publishing Year
Date Published
2023-02-06
Journal Title
arXiv
Article Number
2302.03021
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Cite this

Chen X. Kontsevich’s characteristic classes as topological invariants of configuration space bundles. arXiv. doi:10.48550/ARXIV.2302.03021
Chen, X. (n.d.). Kontsevich’s characteristic classes as topological invariants of configuration space bundles. arXiv. https://doi.org/10.48550/ARXIV.2302.03021
Chen, Xujia. “Kontsevich’s Characteristic Classes as Topological Invariants of Configuration Space Bundles.” ArXiv, n.d. https://doi.org/10.48550/ARXIV.2302.03021.
X. Chen, “Kontsevich’s characteristic classes as topological invariants of configuration space bundles,” arXiv. .
Chen X. Kontsevich’s characteristic classes as topological invariants of configuration space bundles. arXiv, 2302.03021.
Chen, Xujia. “Kontsevich’s Characteristic Classes as Topological Invariants of Configuration Space Bundles.” ArXiv, 2302.03021, doi:10.48550/ARXIV.2302.03021.
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