Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Invertible Dirac operators and handle attachments on manifolds with
  boundary   For spin manifolds with boundary we consider Riemannian metrics which are
product near the boundary and are such that the corresponding Dirac operator is
invertible when half-infinite cylinders are attached at the boundary. The main
result of this paper is that these properties of a metric can be preserved when
the metric is extended over a handle of codimension at least two attached at
the boundary. Applications of this result include the construction of
non-isotopic metrics with invertible Dirac operator, and a concordance
existence and classification theorem.

27
The categories of this paper are: comp-gas
4
The categories of this paper are: cond-mat
6
The categories of this paper are: astro-ph
25
The categories of this paper are: patt-sol
24
The categories of this paper are: dg-ga
10
The categories of this paper are: q-bio
8
The categories of this paper are: hep-ex
13
The categories of this paper are: quant-ph
14
The categories of this paper are: math-ph
35
The categories of this paper are: mtrl-th
15
The categories of this paper are: nucl-ex
7
The categories of this paper are: hep-th
21
The categories of this paper are: adap-org
1
The categories of this paper are: cs
26
The categories of this paper are: bayes-an
29
The categories of this paper are: funct-an