Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A cohomological formula for the Atiyah-Patodi-Singer index on manifolds
  with boundary   We give a cohomological formula for the index of a fully elliptic
pseudodifferential operator on a manifold with boundary. As in the classic case
of Atiyah-Singer, we use an embedding into an euclidean space to express the
index as the integral of a cohomology class depending in this case on a
noncommutative symbol, the integral being over a $C^\infty$-manifold called the
singular normal bundle associated to the embedding. The formula is based on a
K-theoretical Atiyah-Patodi-Singer theorem for manifolds with boundary that is
drawn from Connes' tangent groupoid approach.

6
The categories of this paper are: astro-ph
15
The categories of this paper are: nucl-ex
11
The categories of this paper are: hep-lat
32
The categories of this paper are: atom-ph
3
The categories of this paper are: physics
35
The categories of this paper are: mtrl-th
12
The categories of this paper are: nucl-th
14
The categories of this paper are: math-ph
30
The categories of this paper are: q-alg
4
The categories of this paper are: cond-mat
8
The categories of this paper are: hep-ex
18
The categories of this paper are: econ
26
The categories of this paper are: bayes-an
37
The categories of this paper are: supr-con
29
The categories of this paper are: funct-an
21
The categories of this paper are: adap-org