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

[摘要] 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 XXX. We compute the K1(X)K^1(X)K1(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.

[学科分类] 神经科学

[关键词] Index theory;family index;first order elliptic operators;local boundary conditions