2007
DOI: 10.1017/is007011015jkt011
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Thom isomorphism and push-forward map in twisted K-theory

Abstract: We establish the Thom isomorphism in twisted K-theory for any real vector bundle and develop the push-forward map in twisted K-theory for any differentiable map f : X → Y (not necessarily K-oriented). The push-forward map generalizes the push-forward map in ordinary K-theory for any K-oriented map and the Atiyah-Singer index theorem of Dirac operators on Clifford modules. For D-branes satisfying Freed-Witten's anomaly cancellation condition in a manifold with a non-trivial B-field, we associate a canonical ele… Show more

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Cited by 51 publications
(104 citation statements)
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“…It presents the theory with another point of view and contains some new results. We extend the Thom isomorphism to this more general setting (see also [16]), which is important in order to relate the "ungraded" and "graded" twisted K-theories. We compute many interesting equivariant twisted K-groups, complementing the basic papers [34] We don't pretend to be exhaustive in a subject which has already many ramifications.…”
mentioning
confidence: 99%
“…It presents the theory with another point of view and contains some new results. We extend the Thom isomorphism to this more general setting (see also [16]), which is important in order to relate the "ungraded" and "graded" twisted K-theories. We compute many interesting equivariant twisted K-groups, complementing the basic papers [34] We don't pretend to be exhaustive in a subject which has already many ramifications.…”
mentioning
confidence: 99%
“…Thom isomorphism, which is closely related to Poincaré duality, was established by Karoubi in [11] in the setting of non-twisted K-theory, and by Carey and Wang [5] and Karoubi [12] in twisted K-theory. Let us also mention that (a slight variation) of our main result was obtained independently and simultaneously by Echterhoff, Emerson and Kim [7].…”
Section: * -Algebras Of Continuous Sections C(m A) and C(m Amentioning
confidence: 99%
“…More precisely, we get a natural embedding of the (finite-dimensional) Lie algebras of these stabilizers, into the (infinite-dimensional) loop algebra. The level 1 basic representation of that affine algebra then restricts to a coherent family of projective representations of those stabilizers, and from this the bundle is formed (see Equation (21) in [75]). By using the affine algebra representation, he obtains almost for free a global description of the bundle, avoiding our complicated explicit construction of unitaries and verification of their consistency conditions.…”
Section: The Geometry Of Adjoint Actionsmentioning
confidence: 99%