Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Compact hyperbolic manifolds without spin structures   We exhibit the first examples of compact orientable hyperbolic manifolds that
do not have any spin structure. We show that such manifolds exist in all
dimensions $n \geq 4$. The core of the argument is the construction of a
compact orientable hyperbolic $4$-manifold $M$ that contains a surface $S$ of
genus $3$ with self intersection $1$. The $4$-manifold $M$ has an odd
intersection form and is hence not spin. It is built by carefully assembling
some right angled $120$-cells along a pattern inspired by the minimum
trisection of $\mathbb{C}\mathbb{P}^2$. The manifold $M$ is also the first
example of a compact orientable hyperbolic $4$-manifold satisfying any of these
conditions: 1) $H_2(M,\mathbb{Z})$ is not generated by geodesically immersed
surfaces. 2) There is a covering $\tilde{M}$ that is a non-trivial bundle over
a compact surface.

18
The categories of this paper are: econ
29
The categories of this paper are: funct-an
1
The categories of this paper are: cs
37
The categories of this paper are: supr-con
19
The categories of this paper are: eess
22
The categories of this paper are: chao-dyn
16
The categories of this paper are: stat
13
The categories of this paper are: quant-ph
8
The categories of this paper are: hep-ex
11
The categories of this paper are: hep-lat
27
The categories of this paper are: comp-gas
35
The categories of this paper are: mtrl-th
9
The categories of this paper are: nlin
0
The categories of this paper are: hep-ph
15
The categories of this paper are: nucl-ex
30
The categories of this paper are: q-alg