Differential KO-theory: constructions, computations, and applications
DOI10.1016/j.aim.2021.107671zbMath1476.19007arXiv1809.07059OpenAlexW3150001503MaRDI QIDQ2237344
Hisham Sati, Daniel Joseph Grady
Publication date: 27 October 2021
Published in: Advances in Mathematics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1809.07059
Atiyah-Hirzebruch spectral sequenceAdams operationsRiemann-Roch theoremWhitehead towerWu formuladifferential KO-theory
Characteristic classes and numbers in differential topology (57R20) Homology of classifying spaces and characteristic classes in algebraic topology (55R40) Topological (K)-theory (55N15) Twisted (K)-theory; differential (K)-theory (19L50)
Related Items (4)
Cites Work
- Differential cohomology theories as sheaves of spectra
- \(KO\)-theory of exceptional flag manifolds
- Extended higher cup-product Chern-Simons theories
- Twisted differential string and fivebrane structures
- On Bott-Chern forms and their applications
- T-duality for orientifolds and twisted KR-theory
- Chern classes on differential \(K\)-theory
- Adams operations in smooth \(K\)-theory
- Positive scalar curvature and low-degree group homology
- Elliptic genera, modular forms over \(KO_ *\), and the Brown-Kervaire invariant
- The imbedding problem for Riemannian manifolds
- \(KO\)-theory of complex Stiefel manifolds
- An index theorem in differential \(K\)-theory
- Umkehr maps
- Analytic cycles on complex manifolds
- KO-theory of Hermitian symmetric spaces
- KO-theory of complex Grassmannians
- The order of the differentials in the Atiyah-Hirzebruch spectral sequence
- Complex and real K-theory and localization
- Étale descent for two-primary algebraic \(K\)-theory of totally imaginary number fields
- Monopoles, braid groups, and the Dirac operator
- Five-brane effective action in \(M\)-theory
- Stiefel-Whitney currents.
- Higher-twisted periodic smooth Deligne cohomology
- Primary operations in differential cohomology
- Massey products in differential cohomology via stacks
- Twisted smooth Deligne cohomology
- \(KO\)-theory of flag manifolds
- Universal property of Chern character forms of the canonical connection
- On the integral cohomology of BSpin(n)
- Harmonic spinors
- Topological methods in algebraic geometry. Translation from the German and appendix one by R. L. E. Schwarzenberger. Appendix two by A. Borel.
- \(\mathbb{R} /\mathbb{Z}\) index theory
- Local formulae for Stiefel-Whitney classes
- Čech cocycles for differential characteristic classes: an \(\infty \)-Lie theoretic construction
- Differential \(K\)-theory and localization formula for \(\eta \)-invariants
- Twisted differential generalized cohomology theories and their Atiyah-Hirzebruch spectral sequence
- Spectral sequences in smooth generalized cohomology
- The real \(K\)-theory of compact Lie groups
- The uncertainty of fluxes
- An approach to anomalies in M-theory via KSpin
- Quadratic functions in geometry, topology, and \(M\)-theory
- An Atiyah-Hirzebruch spectral sequence for \(KR\)-theory
- Halbexakte Homotopiefunktoren
- Clifford modules
- \(K_ 0\)-groups of projective spaces
- The structure of the Spin cobordism ring
- The mod 2 cohomology rings of extra-special 2-groups and the spinor groups
- The representation rings of orthogonal groups
- Real bundle gerbes, orientifolds and twisted \(KR\)-homology
- Model Categories of Diagram Spectra
- An elementary differential extension of odd K-theory
- GEOMETRY OF SPIN ANDSPINcSTRUCTURES IN THE M-THEORY PARTITION FUNCTION
- Differential K-Theory: A Survey
- Structured vector bundles define differential K-theory
- TWISTED TOPOLOGICAL STRUCTURES RELATED TO M-BRANES
- Spin structures and superstrings
- Orientifold Precis
- The KO-cohomology ring of SU (2n)/SO (2 n)
- TWISTED TOPOLOGICAL STRUCTURES RELATED TO M-BRANES II: TWISTED Wu ANDWucSTRUCTURES
- A Note on Certain Polynomial Algebras
- On the Cohomology of the Real Grassmann Complexes and the Characteristic Classes of n-Plane Bundles
- FIVEBRANE STRUCTURES
- R/Z-valued index theory via geometric K-homology
- L-infinity algebra connections and applications to String- and Chern-Simons n-transport
- Index theory, eta forms, and Deligne cohomology
- η-Invariants and Their Adiabatic Limits
- The Torsion Pontryagin Classes
- Classifying Spaces for Surgery and Corbordism of Manifolds. (AM-92)
- Higher algebraic K-theory: I
- Characteristic Classes. (AM-76)
- On Thom Spectra, Orientability, and Cobordism
- Symmetric spectra
- The Cohomology of BSO n and BO n with Integer Coefficients
- A Higher Stacky Perspective on Chern–Simons Theory
- Ninebrane structures
- Actions of $K(\pi ,n)$ spaces on $K$-theory and uniqueness of twisted $K$-theory
- Axiomatic characterization of ordinary differential cohomology
- KO-rings of full flag varieties
- Higher Topos Theory (AM-170)
- Riemann-Roch theorems for differentiable manifolds
- K-THEORY AND REALITY
- MODULES OF DIFFERENTIALS OF THE ATIYAH-HIRZEBRUCH SPECTRAL SEQUENCE
- MODULES OF DIFFERENTIALS OF THE ATIYAH-HIRZEBRUCH SPECTRAL SEQUENCE. II
- Integration of simplicial forms and Deligne cohomology
- Existence of Universal Connections
- A note on the 𝐾𝑂-theory of sphere-bundles
- The index of elliptic operators on compact manifolds
- Homotopy Classification of Maps by Cohomology Homomorphisms
- A symmetric ring spectrum representing KO-theory
- Higher-dimensional parallel transports
- A topological proof of real and symplectic Bott periodicity theorem
- Algebraic topology -- homology and homotopy.
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