Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Flat manifolds with holonomy representation of quaternionic type   We are interested in the question of the existence of flat manifolds for
which all $\mathbb R$-irreducible components of the holonomy representation are
either absolutely irreducible, of complex or of quaternionic type. In the first
two cases such examples are well known. But the existence of the third type of
flat manifolds was unknown to the authors. In this article we construct such an
example. Moreover, we present a list of finite groups for which a construction
of manifolds of quaternionic type is impossible.

10
The categories of this paper are: q-bio
5
The categories of this paper are: gr-qc
25
The categories of this paper are: patt-sol
15
The categories of this paper are: nucl-ex
9
The categories of this paper are: nlin
13
The categories of this paper are: quant-ph
36
The categories of this paper are: cmp-lg
28
The categories of this paper are: alg-geom
8
The categories of this paper are: hep-ex
12
The categories of this paper are: nucl-th
16
The categories of this paper are: stat
23
The categories of this paper are: solv-int
19
The categories of this paper are: eess
17
The categories of this paper are: q-fin
37
The categories of this paper are: supr-con
0
The categories of this paper are: hep-ph