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

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