Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Saturated and linear isometric transfer systems for cyclic groups of
  order $p^mq^n$   Transfer systems are combinatorial objects which classify $N_\infty$ operads
up to homotopy. By results of A. Blumberg and M. Hill, every transfer system
associated to a linear isometries operad is also saturated (closed under a
particular two-out-of-three property). We investigate saturated and linear
isometric transfer systems with equivariance group $C_{p^mq^n}$, the cyclic
group of order $p^mq^n$ for $p,q$ distinct primes and $m,n\ge 0$. We give a
complete enumeration of saturated transfer systems for $C_{p^mq^n}$. We also
prove J. Rubin's saturation conjecture for $C_{pq^n}$; this says that every
saturated transfer system is realized by a linear isometries operad for $p,q$
sufficiently large (greater than $3$ in this case).

14
The categories of this paper are: math-ph
21
The categories of this paper are: adap-org
30
The categories of this paper are: q-alg
17
The categories of this paper are: q-fin
25
The categories of this paper are: patt-sol
7
The categories of this paper are: hep-th
10
The categories of this paper are: q-bio
12
The categories of this paper are: nucl-th
22
The categories of this paper are: chao-dyn
9
The categories of this paper are: nlin
24
The categories of this paper are: dg-ga
33
The categories of this paper are: plasm-ph
18
The categories of this paper are: econ
8
The categories of this paper are: hep-ex
35
The categories of this paper are: mtrl-th
13
The categories of this paper are: quant-ph