JournalsjncgOnline First10 November 2022

Self-adjoint local boundary problems on compact surfaces. II. Family index

  • Marina Prokhorova

    Technion - Israel Institute of Technology, Haifa, Israel
Self-adjoint local boundary problems on compact surfaces. II. Family index cover
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Abstract

The paper presents a first step towards a family index theorem for classical self-adjoint boundary value problems.We address here the simplest non-trivial case of manifolds with boundary, namely the case of two-dimensional manifolds. The first result of the paper is an index theorem for families of first order self-adjoint elliptic differential operators with local boundary conditions, parametrized by points of a compact topological space XX. We compute the K1(X)K^1(X)-valued index in terms of the topological data over the boundary. The second result is the universality of the index: we show that the index is a universal additive homotopy invariant for such families if the vanishing on families of invertible operators is assumed.

Cite this article

Marina Prokhorova, Self-adjoint local boundary problems on compact surfaces. II. Family index. J. Noncommut. Geom. (2022), published online first

DOI 10.4171/JNCG/458