Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the K-theoretic classification of topological phases of matter   We present a rigorous and fully consistent $K$-theoretic framework for
studying gapped topological phases of free fermions such as topological
insulators. It utilises and profits from powerful techniques in operator
$K$-theory. From the point of view of symmetries, especially those of time
reversal, charge conjugation, and magnetic translations, operator $K$-theory is
more general and natural than the commutative topological theory. Our approach
is model-independent, and only the symmetry data of the dynamics, which may
include information about disorder, is required. This data is completely
encoded in a suitable $C^*$-superalgebra. From a representation-theoretic point
of view, symmetry-compatible gapped phases are classified by the
super-representation group of this symmetry algebra. Contrary to existing
literature, we do not use $K$-theory to classify phases in an absolute sense,
but only relative to some arbitrary reference. $K$-theory groups are better
thought of as groups of obstructions between homotopy classes of gapped phases.
Besides rectifying various inconsistencies in the existing literature on
$K$-theory classification schemes, our treatment has conceptual simplicity in
its treatment of all symmetries equally. The Periodic Table of Kitaev is
exhibited as a special case within our framework, and we prove that the
phenomena of periodicity and dimension shifts are robust against disorder and
magnetic fields.

36
The categories of this paper are: cmp-lg
9
The categories of this paper are: nlin
11
The categories of this paper are: hep-lat
30
The categories of this paper are: q-alg
17
The categories of this paper are: q-fin
23
The categories of this paper are: solv-int
6
The categories of this paper are: astro-ph
12
The categories of this paper are: nucl-th
22
The categories of this paper are: chao-dyn
16
The categories of this paper are: stat
10
The categories of this paper are: q-bio
32
The categories of this paper are: atom-ph
18
The categories of this paper are: econ
21
The categories of this paper are: adap-org
20
The categories of this paper are: acc-phys
26
The categories of this paper are: bayes-an