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ETA INVARIANTS FOR MANIFOLD WITH BOUNDARY

    Supported in part by the NSF.

    https://doi.org/10.1142/9789812773609_0007Cited by:0 (Source: Crossref)
    Abstract:

    For a compact manifold with boundary, M, there are well known local boundary conditions that make the de Rham operator A = d+δ elliptic, namely the absolute and relative boundary conditions. We study the eta invariants of such elliptic boundary value problems under the metric deformation

    where x ɛ C(M) is, near the boundary, the geodesic distance to the boundary, and g is a Riemannian metric on M which is of product type near the boundary. Under certain acyclicity condition we show that when M is odd dimensional
    where the subscript a (r) indicates the absolute (relative) boundary condition, and ηb(A0) is the b-eta invariant of the limiting operator A0. If M is even dimensional then
    Most of the analysis extends to analytic torsion, yielding
    when dim M is odd, and
    when dim M is even. Here the sign ± depends on the choice of the boundary condition and r1 , r2 vanishes at ɛ = 0.

    Dedication: Dedicated to Krzysztof P. Wojciechowski on his 50th birthday
    Keywords:
    AMSC: Primary 58J28, Secondary 35J25