2026-09-22T22:54:09Zhttps://api.repository.cam.ac.uk/server/oai/requestoai:www.repository.cam.ac.uk:1810/3178922023-12-22T12:56:40Zcom_1810_213747com_1810_256064col_1810_213748
On tautological classes of fibre bundles and self-embedding calculus
10.17863/CAM.65008
Prigge, Nils
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Randal-Williams, Oscar
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In this thesis we study the ring of characteristic classes of smooth fibre bundles with a particular focus on tautological classes and the ring that they generate. In the first part we use tools from rational homotopy theory to compute analogues of tautological rings over fibrations, which provides upper bounds on the tautological rings of fibre bundles. In some cases we find an upper bound on the Krull dimension that is sharp.
In the second part, we study the classifying space using the calculus of embeddings which provides a homotopy theoretic approximation. We construct cohomology classes on the self-embedding tower which extend certain characteristic classes that were introduced by Kontsevich. This construction is based on introducing configuration space integrals over the tower itself, which also has some consequences for tautological classes that we explore.
University of Cambridge
2020-07-06
Thesis
Doctoral
eng
Cambridge Trust and King's College Martin Thackeray Scholarship
https://www.repository.cam.ac.uk/handle/1810/317892
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Algebraic Topology
Characteristic Classes
Embedding Calculus
Fibre Bundles