Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Invertible phases of matter with spatial symmetry   We propose a general formula for the group of invertible topological phases
on a space $Y$, possibly equipped with the action of a group $G$. Our formula
applies to arbitrary symmetry types. When $Y$ is Euclidean space and $G$ a
crystallographic group, the term `topological crystalline phases' is sometimes
used for these phases of matter.

25
The categories of this paper are: patt-sol
28
The categories of this paper are: alg-geom
3
The categories of this paper are: physics
15
The categories of this paper are: nucl-ex
22
The categories of this paper are: chao-dyn
9
The categories of this paper are: nlin
13
The categories of this paper are: quant-ph
16
The categories of this paper are: stat
31
The categories of this paper are: ao-sci
10
The categories of this paper are: q-bio
26
The categories of this paper are: bayes-an
32
The categories of this paper are: atom-ph
37
The categories of this paper are: supr-con
29
The categories of this paper are: funct-an
5
The categories of this paper are: gr-qc
35
The categories of this paper are: mtrl-th