Differential cohomology (encyclopedia article)

Abstract

We give an overview of differential cohomology from the point of view of algebraic topology. This includes a survey of several different definitions of differential cohomology groups, a discussion of differential characteristic classes, an introduction to differential generalized cohomology theory, and some applications in physics.

arXiv comment20 pages, article for the Encyclopedia of Mathematical Physics, 2nd ed

References in corpus (47)

• Symmetry-protected topological orders for interacting fermions -- Fermionic topological nonlinear $\sigma$ models and a special group supercohomology theory
• Reflection positivity and invertible topological phases
• Fermionic SPT phases in higher dimensions and bosonization
• The Uncertainty of Fluxes
• Heisenberg Groups and Noncommutative Fluxes
• Twisted differential String and Fivebrane structures
• Symmetry Protected Topological phases and Generalized Cohomology
• Čech cocycles for differential characteristic classes -- An infinity-Lie theoretic construction
• Construction and classification of symmetry protected topological phases in interacting fermion systems
• Axiomatic Characterization of Ordinary Differential Cohomology
• Equivariant Cohomotopy implies orientifold tadpole cancellation
• Twisted Cohomotopy implies M-theory anomaly cancellation on 8-manifolds
• The WZW term of the M5-brane and differential cohomotopy
• Framed M-branes, corners, and topological invariants
• Structured vector bundles define differential K-theory
• Twisted Cohomotopy implies level quantization of the full 6d Wess-Zumino term of the M5-brane
• Twisted Cohomotopy implies twisted String structure on M5-branes
• Differential Cohomotopy implies intersecting brane observables via configuration spaces and chord diagrams
• Type II Actions from 11-Dimensional Chern-Simons Theories
• Twistorial Cohomotopy implies Green-Schwarz anomaly cancellation
• Ramond-Ramond Fields, Fractional Branes and Orbifold Differential K-Theory
• Differential cohomotopy versus differential cohomology for M-theory and differential lifts of Postnikov towers
• Lift of fractional D-brane charge to equivariant Cohomotopy theory
• T-duality For Orientifolds and Twisted KR-theory
• Massey products in differential cohomology via stacks
• Anyonic Defect Branes and Conformal Blocks in Twisted Equivariant Differential (TED) K-theory
• Primary operations in differential cohomology
• Hodge filtered complex bordism
• Regulators and cycle maps in higher-dimensional differential algebraic K-theory
• The $\mathbb{R}$-Local Homotopy Theory of Smooth Spaces
• T-duality and Differential K-Theory
• A Geometric Model for Odd Differential K-theory
• Differential models for the Anderson dual to bordism theories and invertible QFT's, II
• Landweber exact formal group laws and smooth cohomology theories
• Flux Quantization on Phase Space
• Differential models for the Anderson dual to bordism theories and invertible QFT's, I
• Multiplicative differential algebraic K-theory and applications
• Foliated manifolds, algebraic K-theory, and a secondary invariant
• The Caloron Correspondence and Odd Differential K-theory
• A smooth variant of Hopkins-Singer differential K-theory
• Parametrized geometric cobordism and smooth Thom stacks
• Twisted differential K-characters and D-branes
• Unstable splittings in Hodge filtered Brown-Peterson cohomology
• Smooth classifying spaces for differential $K$-theory
• Constructing the Virasoro groups using differential cohomology
• Invertible QFTs and differential Anderson duals
• Deformation classes of invertible field theories and the Freed--Hopkins conjecture

Cited by in corpus (1)

• Primary operations in differential cohomology