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251
The Equivariant Noncommutative AtiyahPatodiSinger Index Theorem ∗
, 2006
"... In [Wu], the noncommutative AtiyahPatodiSinger index theorem was proved. In this paper, we extend this theorem to the equivariant case. Keywords: Equivariant total eta invariants; Clifford asymptotics; C(1)Fredholm module; superconnection. ..."
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Cited by 1 (1 self)
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In [Wu], the noncommutative AtiyahPatodiSinger index theorem was proved. In this paper, we extend this theorem to the equivariant case. Keywords: Equivariant total eta invariants; Clifford asymptotics; C(1)Fredholm module; superconnection.
A noncommutative AtiyahPatodiSinger index theorem in KKtheory
, 2007
"... We investigate an extension of ideas of AtiyahPatodiSinger (APS) to a noncommutative geometry setting framed in terms of Kasparov modules. We use a mapping cone construction to relate odd index pairings to even index pairings with APS boundary conditions in the setting of KKtheory, generalising t ..."
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Cited by 11 (6 self)
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We investigate an extension of ideas of AtiyahPatodiSinger (APS) to a noncommutative geometry setting framed in terms of Kasparov modules. We use a mapping cone construction to relate odd index pairings to even index pairings with APS boundary conditions in the setting of KKtheory, generalising
SPECTRAL SECTIONS AND HIGHER ATIYAHPATODISINGER INDEX THEORY ON GALOIS COVERINGS
 GAFA GEOMETRIC AND FUNCTIONAL ANALYSIS
, 1998
"... In this paper we consider Γ → ˜ M → M, a Galois covering with boundary and ˜ D/, a Γinvariant generalized Dirac operator on ˜M. We assume that the group Γ is of polynomial growth with respect to a word metric. By employing the notion of noncommutative spectral section associated to the boundary op ..."
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Cited by 20 (7 self)
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operator ˜ D/ 0 and the bcalculus on Galois coverings with boundary, we develop a higher AtiyahPatodiSinger index theory. Our main theorem extends to such ΓGalois coverings with boundary the higher index theorem of ConnesMoscovici.
Cyclic homology and the AtiyahPatodiSinger index theorem
 In Index theory and operator algebras
, 1991
"... Abstract. We apply the boundary pseudodifferential calculus of Melrose to study the Chern character in entire cyclic homology of the Dirac operator of a manifold with boundary. Recently, Melrose has proved the AtiyahPatodiSinger index theorem using a calculus of pseudodifferential operators for ma ..."
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Cited by 14 (0 self)
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Abstract. We apply the boundary pseudodifferential calculus of Melrose to study the Chern character in entire cyclic homology of the Dirac operator of a manifold with boundary. Recently, Melrose has proved the AtiyahPatodiSinger index theorem using a calculus of pseudodifferential operators
On The Arnold Conjecture And The AtiyahPatodiSinger Index Theorem
, 1999
"... The Arnold conjecture yields a lower bound to the number of periodic classical trajectories in a Hamiltonian system. Here we count these trajectories with the help of a path integral, which we inspect using properties of the spectral flow of a Dirac operator in the background of a Sp(2N) valued gaug ..."
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gauge field. We compute the spectral flow from the AtiyahPatodiSinger index theorem, and apply the results to evaluate the path integral using localization methods. In this manner we find a lower bound to the number of periodic classical trajectories which is consistent with the Arnold conjecture.
THE ATIYAHPATODISINGER INDEX THEOREM FOR DIRAC OPERATORS OVER C∗ALGEBRAS
, 2009
"... We prove an AtiyahPatodiSinger index theorem for Dirac operators twisted by C ∗vector bundles. We use it to derive a general product formula for ηforms and to define and study new ρinvariants generalizing Lott’s higher ρform. The higher AtiyahPatodiSinger index theorem of LeichtnamPiazza ca ..."
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Cited by 5 (3 self)
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We prove an AtiyahPatodiSinger index theorem for Dirac operators twisted by C ∗vector bundles. We use it to derive a general product formula for ηforms and to define and study new ρinvariants generalizing Lott’s higher ρform. The higher AtiyahPatodiSinger index theorem of Leichtnam
Real embeddings and the AtiyahPatodiSinger index theorem for Dirac operators
 ASIAN J. MATH
, 2008
"... We present the details of our embedding proof, which was announced in [DZ1], of the AtiyahPatodiSinger index theorem for Dirac operators on manifolds with boundary [APS1]. ..."
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Cited by 4 (1 self)
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We present the details of our embedding proof, which was announced in [DZ1], of the AtiyahPatodiSinger index theorem for Dirac operators on manifolds with boundary [APS1].
A Higher Atiyah–Patodi–Singer index theorem for the signature operator
 on Galois Coverings, Ann. Global Anal. Geom
"... Abstract. Let (N, g) be a closed Riemannian manifold of dimension 2m − 1andletƔ→Ñ → N be a Galois covering of N. We assume that Ɣ is of polynomial growth with respect to a word metric and that �Ñ is L2invertible in degree m. By employing spectral sections with a symmetry property with respect to th ..."
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Cited by 10 (5 self)
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on � ∂ ˜M, and always employing symmetric spectral sections, we define a canonical Atiyah–Patodi–Singer index class, in K0(C ∗ r (Ɣ)), for the signature operator of ˜M. Using the higher APS index theory developed in [6], we express the Chern character of this index class in terms of a local integral
Results 1  10
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251