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 . We compute the -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. 16 (2022), no. 4, pp. 1213–1257DOI 10.4171/JNCG/458