On tautological classes of fibre bundles and self-embedding calculus
type: CreativeWork
description: 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.
abstract: 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.
author: Prigge, Nils
language: eng
keywords: Algebraic Topology, Characteristic Classes, Embedding Calculus, Fibre Bundles
license: https://apollo8-f-pro.lib.cam.ac.uk/bitstreams/942a89d7-901d-47ba-a385-411a08859691/download
license: https://www.rioxx.net/licenses/all-rights-reserved/
date published: 2020-07-06
date modified: 2026-07-22T22:24:00Z
provider: Cambridge University
publisher: Networked Digital Library of Theses and Dissertations
type: WebPage
source organization: University of Cambridge

PropertyValue
property ID: DOI
value: 10.17863/CAM.65008