Academic
Publications
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

Spectral asymmetry and Riemannian geometry. III   (Citations: 619)
BibTex | RIS | RefWorks Download
Cumulative Annual
View Publication
The following links allow you to view full publications. These links are maintained by other sources not affiliated with Microsoft Academic Search.
    • ...Proof. For part (1), write F F; hF ;rR; . By the Atiyah-Patodi-Singer index theorem [3],...

    Daniel S. Freedet al. An index theorem in differential K–theory

    • ...Using Claim 4.2, and the Atiyah-Patodi-Singer index formula [1] on manifolds with boundary, Dai and Wei proved in [7] the following theorem for manifolds with fibred cuspidal infinity:...

    Fuquan Fanget 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 L2-solutions’ 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 self-adjoint we will follow the basic strategy of [1] and display a parametrix which is (almost) an exact inverse...

    A. L. Careyet al. Noncommutative Atiyah-Patodi-Singer 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 Mülleret al. Scattering at Low Energies on Manifolds with Cylindrical Ends and Stab...

    • ...of the family of self-adjoint 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. Nazaikinskiiet al. On the Poincaré isomorphism in K -theory on manifolds with edges

Sort by: