Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Differential K-theory. A survey   Generalized differential cohomology theories, in particular differential
K-theory (often called "smooth K-theory"), are becoming an important tool in
differential geometry and in mathematical physics. In this survey, we describe
the developments of the recent decades in this area. In particular, we discuss
axiomatic characterizations of differential K-theory (and that these uniquely
characterize differential K-theory). We describe several explicit
constructions, based on vector bundles, on families of differential operators,
or using homotopy theory and classifying spaces. We explain the most important
properties, in particular about the multiplicative structure and push-forward
maps and will state versions of the Riemann-Roch theorem and of Atiyah-Singer
family index theorem for differential K-theory.

22
The categories of this paper are: chao-dyn
13
The categories of this paper are: quant-ph
36
The categories of this paper are: cmp-lg
18
The categories of this paper are: econ
19
The categories of this paper are: eess
0
The categories of this paper are: hep-ph
27
The categories of this paper are: comp-gas
9
The categories of this paper are: nlin
32
The categories of this paper are: atom-ph
33
The categories of this paper are: plasm-ph
8
The categories of this paper are: hep-ex
31
The categories of this paper are: ao-sci
21
The categories of this paper are: adap-org
5
The categories of this paper are: gr-qc
14
The categories of this paper are: math-ph
20
The categories of this paper are: acc-phys