Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Closed manifolds with transcendental L2-Betti numbers   In this paper, we show how to construct examples of closed manifolds with
explicitly computed irrational, even transcendental L2 Betti numbers, defined
via the universal covering.
  We show that every non-negative real number shows up as an L2-Betti number of
some covering of a compact manifold, and that many computable real numbers
appear as an L2-Betti number of a universal covering of a compact manifold
(with a precise meaning of computable given below).
  In algebraic terms, for many given computable real numbers (in particular for
many transcendental numbers) we show how to construct a finitely presented
group and an element in the integral group ring such that the L2-dimension of
the kernel is the given number.
  We follow the method pioneered by Austin in "Rational group ring elements
with kernels having irrational dimension" arXiv:0909.2360) but refine it to get
very explicit calculations which make the above statements possible.

17
The categories of this paper are: q-fin
6
The categories of this paper are: astro-ph
22
The categories of this paper are: chao-dyn
33
The categories of this paper are: plasm-ph
8
The categories of this paper are: hep-ex
28
The categories of this paper are: alg-geom
19
The categories of this paper are: eess
18
The categories of this paper are: econ
27
The categories of this paper are: comp-gas
9
The categories of this paper are: nlin
23
The categories of this paper are: solv-int
15
The categories of this paper are: nucl-ex
20
The categories of this paper are: acc-phys
4
The categories of this paper are: cond-mat
3
The categories of this paper are: physics
37
The categories of this paper are: supr-con