Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The two definitions of the index difference   Given two metrics of positive scalar curvature metrics on a closed spin
manifold, there is a secondary index invariant in real $K$-theory. There exist
two definitions of this invariant, one of homotopical flavour, the other one
defined by a index problem of Atiyah-Patodi-Singer type. We give a complete and
detailed proof of the folklore result that both constructions yield the same
answer. Moreover, we generalize this to the case of two families of positive
scalar curvature metrics, parametrized by a compact space. In essence, we prove
a generalization of the classical "spectral-flow-index theorem" to the case of
families of real operators.

5
The categories of this paper are: gr-qc
7
The categories of this paper are: hep-th
18
The categories of this paper are: econ
11
The categories of this paper are: hep-lat
15
The categories of this paper are: nucl-ex
26
The categories of this paper are: bayes-an
32
The categories of this paper are: atom-ph
25
The categories of this paper are: patt-sol
4
The categories of this paper are: cond-mat
17
The categories of this paper are: q-fin
3
The categories of this paper are: physics
22
The categories of this paper are: chao-dyn
37
The categories of this paper are: supr-con
33
The categories of this paper are: plasm-ph
23
The categories of this paper are: solv-int
14
The categories of this paper are: math-ph