Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Self-adjoint local boundary problems on compact surfaces. II. Family
  index   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 $X$. We compute the
$K^1(X)$-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 required.

18
The categories of this paper are: econ
15
The categories of this paper are: nucl-ex
13
The categories of this paper are: quant-ph
34
The categories of this paper are: chem-ph
8
The categories of this paper are: hep-ex
20
The categories of this paper are: acc-phys
28
The categories of this paper are: alg-geom
29
The categories of this paper are: funct-an
22
The categories of this paper are: chao-dyn
11
The categories of this paper are: hep-lat
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The categories of this paper are: patt-sol
32
The categories of this paper are: atom-ph
6
The categories of this paper are: astro-ph
27
The categories of this paper are: comp-gas
23
The categories of this paper are: solv-int
21
The categories of this paper are: adap-org