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An index theorem in differential ktheory
"... Abstract. Let π: X�Bbe a proper submersion with a Riemannian structure. Given a differential Ktheory class on X, we define its analytic and topological indices as differential Ktheory classes on B. We prove that the two indices are the same. 1. ..."
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Abstract. Let π: X�Bbe a proper submersion with a Riemannian structure. Given a differential Ktheory class on X, we define its analytic and topological indices as differential Ktheory classes on B. We prove that the two indices are the same. 1.
An elementary differential extension of odd Ktheory
 Journal of Ktheory: Ktheory and its Applications to Algebra, Geometry, and Topology, FirstView:1–31
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Differential equivariant Ktheory
"... Following Hopkins and Singer, we give a definition for the differential equivariant Ktheory of a smooth manifold acted upon by a finite group. The ring structure for differential equivariant Ktheory is developed explicitly. We also construct a pushforward map which parallels the topological pushfo ..."
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Following Hopkins and Singer, we give a definition for the differential equivariant Ktheory of a smooth manifold acted upon by a finite group. The ring structure for differential equivariant Ktheory is developed explicitly. We also construct a pushforward map which parallels the topological pushforward in equivariant Ktheory. An analytic formula for the pushforward to the differential equivariant Ktheory of a point is conjectured, and proved in the boundary case, in the case of a free action, and for ordinary differential Ktheory in general. The latter proof is due to K. Klonoff. 1
On Bott–Chern forms and their applications
, 2013
"... On Bott–Chern forms and their ..."
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The universal ηinvariant for manifolds with boundary
, 2014
"... We extend the theory of the universal ηinvariant to the case of relative bordism groups of manifolds with boundaries. This allows the construction of secondary descendants of the universal ηinvariant. We obtain an interpretation of Laures’ finvariant as an example of this general construction. ..."
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We extend the theory of the universal ηinvariant to the case of relative bordism groups of manifolds with boundaries. This allows the construction of secondary descendants of the universal ηinvariant. We obtain an interpretation of Laures’ finvariant as an example of this general construction.