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Keywords
(1)
riemannian geometry
Related Publications
(45)
Selfadjoint elliptic operators and manifold decompositions
symplectic reduction in a symplectic Hilbert space and a splitting formula for spectral flow
Unitary Representations of Brieskorn Spheres
The AtiyahPatod...
The analysis of elliptic families
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Spectral asymmetry and Riemannian geometry. III
Spectral asymmetry and Riemannian geometry. III,10.1017/S0305004100052105,Mathematical Proceedings of The Cambridge Philosophical Society,M. F. Atiyah
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Spectral asymmetry and Riemannian geometry. III
(
Citations: 619
)
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M. F. Atiyah
,
V. K. Patodi
,
I. M. Singer
Journal:
Mathematical Proceedings of The Cambridge Philosophical Society  MATH PROC CAMBRIDGE PHIL SOC
, vol. 79, no. 01, 1976
DOI:
10.1017/S0305004100052105
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(
www.csee.wvu.edu
)
(
www.journals.cambridge.org
)
Citation Context
(252)
...Proof. For part (1), write F F; hF ;rR; . By the AtiyahPatodiSinger index theorem [
3
],...
Daniel S. Freed
,
et al.
An index theorem in differential K–theory
...Using Claim 4.2, and the AtiyahPatodiSinger index formula [
1
] on manifolds with boundary, Dai and Wei proved in [7] the following theorem for manifolds with fibred cuspidal infinity:...
Fuquan Fang
,
et al.
Nonsingular Solutions of Normalized Ricci Flow on Noncompact Manifolds...
...It is necessary to single out the zero eigenvalue ofD for special attention since it gives rise to ‘extended L2solutions’ which contribute to the index, [
1
]...
...The domain of @t +D is dened similarly using 1 P in place of P . Then it can be shown, see for instance [
1
], that ^...
...M(C;C(X)) determined by the unitary u over C(X), so that [eu] [
1
]2 K0(M(C;C(X)))...
...and negative spectral projections for v1: Then for t2 [0;
1
] dene v2(t) = p+ +eit p...
...so that we have a continuous path of unitaries from the identity (t = 0) to v1 (t = 1). Observe that v2(t) is unitary for all t2 [0;
1
], v22 C([0; 1]) M2m(A), v2(0) = 1 and v2(1) = v1. Now dene...
...so that we have a continuous path of unitaries from the identity (t = 0) to v1 (t = 1). Observe that v2(t) is unitary for all t2 [0; 1], v22 C([0;
1
]) M2m(A), v2(0) = 1 and v2(1) = v1. Now dene...
...(ii) If v(t); t2 [0;
1
] is a continuous path in V (F;A) then v(0) v(1)...
...D is selfadjoint we will follow the basic strategy of [
1
] and display a parametrix which is (almost) an exact inverse...
A. L. Carey
,
et al.
Noncommutative AtiyahPatodiSinger boundary conditions and index pair...
...That is, ψ is a limiting value of 12F(ψ,0) in the sense of Atiyah, Patodi, and Singer ([
APS75
])...
Werner Müller
,
et al.
Scattering at Low Energies on Manifolds with Cylindrical Ends and Stab...
...of the family of selfadjoint Dirac operators on fibers is defined (see, e.g., [
4
].) This family is parameterized by points of the base X. We assume that the following condition holds...
V. E. Nazaikinskii
,
et al.
On the Poincaré isomorphism in K theory on manifolds with edges
References
(15)
On the heat equation and the index theorem
(
Citations: 193
)
M. Atiyah
,
R. Bott
,
V. K. Patodi
Journal:
Inventiones Mathematicae  INVENT MATH
, vol. 19, no. 4, pp. 279330, 1973
The index of elliptic operators III
(
Citations: 331
)
M. F. Atiyah
,
I. M. Singer
Published in 1968.
Some cohomology classes in principal ber bundles and their application to riemannian geometry
(
Citations: 14
)
Shiing Shen Chern
,
James Simons
Journal:
Proceedings of The National Academy of Sciences  PNAS
, 1971
Seminar on the Atiyah  Singer Index Theorem
(
Citations: 109
)
R. Palais
Published in 1965.
Analytic extension of the trace associated with elliptic boundary value problems
(
Citations: 44
)
R. T. Seeley
Published in 1969.
Sort by:
Citations
(619)
Spectral triples and manifolds with boundary
(
Citations: 1
)
Bruno Iochum
,
Cyril Levy
Journal:
Journal of Functional Analysis  J FUNCT ANAL
, vol. 260, no. 1, pp. 117134, 2011
Corners in Mtheory
(
Citations: 1
)
Hisham Sati
Journal:
Journal of Physics Amathematical and Theoretical  J PHYS AMATH THEOR
, vol. 44, no. 25, 2011
Global boundary conditions for a Dirac operator on the solid torus
Slawomir Klimek
,
Matt McBride
Journal:
Journal of Mathematical Physics  J MATH PHYSNY
, vol. 52, no. 6, pp. 3518063518, 2011
Eta cocycles, relative pairings and the GodbillonVey index theorem
Hitoshi Moriyoshi
,
Paolo Piazza
Published in 2011.
Classical limit of the dbar operators on quantum domains
Slawomir Klimek
,
Matt McBride
Published in 2011.