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11
Weyl laws on open manifolds
 Math. Annalen
"... Abstract. Under suitable invertibility hypothesis, the spectrum of the Dirac operator on certain open spin Riemannian manifolds is discrete, and obeys a growth law depending qualitatively on the (in)finiteness of the volume. 1. ..."
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Abstract. Under suitable invertibility hypothesis, the spectrum of the Dirac operator on certain open spin Riemannian manifolds is discrete, and obeys a growth law depending qualitatively on the (in)finiteness of the volume. 1.
Adiabatic limits of eta and zeta functions of elliptic operators
 MATHEMATISCHE ZEITSCHRIFT
, 2008
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Adiabatic limit of the Eta invariant over cofinite quotient of PSL(2
 R), Comp. Math
"... Abstract. We study the adiabatic limit of the eta invariant of the Dirac operator over cofinite quotient of PSL(2, R), which is a noncompact manifold with a nonexact fibredcusp metric near the ends. 1. ..."
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Abstract. We study the adiabatic limit of the eta invariant of the Dirac operator over cofinite quotient of PSL(2, R), which is a noncompact manifold with a nonexact fibredcusp metric near the ends. 1.
Gravitational and axial anomalies for generalized Euclidean TaubNUT metrics
 J. Phys. A – Math. Gen
"... The gravitational anomalies are investigated for generalized Euclidean TaubNUT metrics which admit hidden symmetries analogous to the RungeLenz vector of the Keplertype problem. In order to evaluate the axial anomalies, the index of the Dirac operator for these metrics with the APS boundary condi ..."
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The gravitational anomalies are investigated for generalized Euclidean TaubNUT metrics which admit hidden symmetries analogous to the RungeLenz vector of the Keplertype problem. In order to evaluate the axial anomalies, the index of the Dirac operator for these metrics with the APS boundary condition is computed. The role of the KillingYano tensors is discussed for these two types of quantum anomalies. Pacs: 04.62.+v 1
Quantum anomalies for generalized Euclidean TaubNUT metrics
"... We investigate quantum anomalies for generalized Euclidean TaubNUT metrics which admit hidden symmetries analogous to the RungeLenz vector of the Keplertype problem. We review results which show that the appearance of gravitational anomalies is connected with the absence of KillingYano tensors f ..."
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We investigate quantum anomalies for generalized Euclidean TaubNUT metrics which admit hidden symmetries analogous to the RungeLenz vector of the Keplertype problem. We review results which show that the appearance of gravitational anomalies is connected with the absence of KillingYano tensors for these metrics. We have found that for axial anomalies the presence of KillingYano tensors is irrelevant. In order to evaluate the axial anomalies, the index of the Dirac operator with the APS boundary condition is computed on balls and on annular domains, in terms of the radii of the domain. Pacs: 04.62.+v 1
REGULARITY OF THE ETA FUNCTION ON MANIFOLDS WITH CUSPS
, 901
"... Abstract. On a spin manifold with conformal cusps, we prove under an invertibility condition at infinity that the eta function of the twisted Dirac operator has at most simple poles and is regular at the origin. For hyperbolic manifolds of finite volume, the eta function of the Dirac operator twiste ..."
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Abstract. On a spin manifold with conformal cusps, we prove under an invertibility condition at infinity that the eta function of the twisted Dirac operator has at most simple poles and is regular at the origin. For hyperbolic manifolds of finite volume, the eta function of the Dirac operator twisted by any homogeneous vector bundle is shown to be entire. 1.
Bott Periodicity for Fibred Cusp Operators
, 2005
"... In the framework of fibred cusp operators on a manifold X associated to a boundary fibration Φ: ∂X → Y, the homotopy groups of the space G−∞Φ (X;E) of invertible smoothing perturbations of the identity are computed in terms of the Ktheory of T ∗Y. It is shown that there is a periodicity, namely the ..."
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In the framework of fibred cusp operators on a manifold X associated to a boundary fibration Φ: ∂X → Y, the homotopy groups of the space G−∞Φ (X;E) of invertible smoothing perturbations of the identity are computed in terms of the Ktheory of T ∗Y. It is shown that there is a periodicity, namely the odd and the even homotopy groups are isomorphic among themselves. To obtain this result, one of the important steps is the description of the index of a Fredholm smoothing perturbation of the identity in terms of an associated Kclass in K0c (T ∗Y).
Contents
, 2008
"... Discrete optic breathers in zigzag chain: analytical study and ..."
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On Carvalho's Ktheoretic formulation of the cobordism invariance of the index
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