Chern–Weil forms and abstract homotopy theory

DOI10.1090/S0273-0979-2013-01415-0zbMath1281.58001arXiv1301.5959WikidataQ125945383 ScholiaQ125945383MaRDI QIDQ2849009

Daniel S. Freed, Michael J. Hopkins

Publication date: 16 September 2013

Published in: Bulletin of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1301.5959

zbMATH Keywords

de Rham complexhomotopyChern-Weil theoryuniversal connectionuniversal space of differential forms

Mathematics Subject Classification ID

Abstract and axiomatic homotopy theory in algebraic topology (55U35) Connections (general theory) (53C05) (G)-structures (53C10) Differential geometric aspects of gerbes and differential characters (53C08) Topos-theoretic approach to differentiable manifolds (58A03)

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Cites Work

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• Survey article: an elementary illustrated introduction to simplicial sets
• The localization of spectra with respect to homology
• The geometric realization of a semi-simplicial complex
• Derived smooth manifolds
• The moment map and equivariant cohomology
• Superconnections and the Chern character
• Superconnections, Thom classes, and equivariant differential forms
• Universal connections
• On the space of maps inducing isomorphic connections
• A remark on universal connections
• Sheaves in geometry and logic: a first introduction to topos theory
• The localization of spaces with respect to homology
• Characteristic forms and geometric invariants
• Čech cocycles for differential characteristic classes: an \(\infty \)-Lie theoretic construction
• Relative quantum field theory
• Quadratic functions in geometry, topology, and \(M\)-theory
• Homotopical algebra
• Rational homotopy theory
• Classifying spaces and spectral sequences
• Seminar of algebraic geometry du Bois-Marie 1963--1964. Topos theory and étale cohomology of schemes (SGA 4). Vol. 1: Topos theory. Exp. I--IV
• Equations différentielles à points singuliers réguliers
• On the heat equation and the index theorem
• An introduction to d-manifolds and derived differential geometry
• The Verdier Hypercovering Theorem
• Index theory, eta forms, and Deligne cohomology
• Characteristic Classes. (AM-76)
• Regulators and characteristic classes of flat bundles
• Abstract homotopy theory and generalized sheaf cohomology
• Existence of Universal Connections II
• Simplicial homotopy theory
• Simplicial homotopy theory