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Using basic homotopy constructions, we show that isomorphism classes of string structures on spin bundles are naturally given by certain degree 3 cohomology classes, which we call string classes, on the total space of the bundle.
Homologie singulière des espaces fibrés. Applications
Jean-Pierre Serre · 1951
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Laplacien sur une variété riemannienne et spineurs
André Lichnerowicz · 1962
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Compact Lie groups and the stable homotopy of spheres
M. F. Atiyah and L. Smith · 1974
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Characteristic forms and geometric invariants
Shiing Shen Chern and James Simons · 1974
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Harmonic spinors
Nigel Hitchin · 1974
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Curvatures of left invariant metrics on Lie groups
John Milnor · 1976
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Differential characters and geometric invariants
Jeff Cheeger and James Simons · 1985
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Elliptic cohomology (after Landweber-Stong, Ochanine, Witten, and others)
Graeme Segal · 1988
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The index of the Dirac operator in loop space
Edward Witten · 1988
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String structures on loop bundles
R. Coquereaux and K. Pilch · 1989
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Spin geometry
H. Blaine Lawson, Jr. and Marie-Louise Michelsohn · 1989
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The adiabatic limit, Hodge cohomology and Leray’s spectral sequence for a fibration
Rafe R. Mazzeo and Richard B. Melrose · 1990
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Adiabatic limits, nonmultiplicativity of signature, and Leray spectral sequence
Xianzhe Dai · 1991
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Simply connected manifolds of positive scalar curvature
Stephan Stolz · 1992
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Spectral sequences and adiabatic limits
Robin Forman · 1995
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Classical Chern-Simons theory. I
Daniel S. Freed · 1995
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Modular forms and topology
Kefeng Liu · 1996
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A conjecture concerning positive Ricci curvature and the Witten genus
Two-vector bundles and forms of elliptic cohomology
Nils A. Baas, Bjorn Ian Dundas, and John Rognes · 2004
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Conformal field theory and elliptic cohomology
P. Hu and I. Kriz · 2004
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What is an elliptic object?
Stephan Stolz and Peter Teichner · 2004
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Canonical metric connections associated to string structures
Corbett Redden · 2006
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From loop groups to 2-groups
John C. Baez, Danny Stevenson, Alissa S. Crans, and Urs Schreiber · 2007
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Integrating L ∞ L_{\infty} -algebras
André Henriques · 2008
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Harmonic forms on principal bundles, 2008
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Stephan Stolz · 1996
Cited alongside, same era.
Index of Dirac operators
Edward Witten · 1999
Cited alongside, same era.
Beyond the elliptic genus
Orlando Alvarez and I. M. Singer · 2002
Cited alongside, same era.
Classical Chern-Simons theory. II
Daniel S. Freed · 2002
Cited alongside, same era.
Algebraic topology and modular forms
M. J. Hopkins · 2002
Cited alongside, same era.
Corbett Redden · 2008
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Axiomatic characterization of ordinary differential cohomology
James Simons and Dennis Sullivan · 2008
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A finite-dimensional string 2-group, 2009
Christopher Schommer-Pries · 2009
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String connections and chern-simons theory, 2009
Konrad Waldorf · 2009
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