Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A pro-algebraic fundamental group for topological spaces   Consider a connected topological space $X$ with a point $x \in X$ and let $K$
be a field with the discrete topology. We study the Tannakian category of
finite dimensional (flat) vector bundles on $X$ and its Tannakian dual $\pi_K
(X,x)$ with respect to the fibre functor in $x$. The maximal pro-\'etale
quotient of $\pi_K (X,x)$ is the \'etale fundamental group of $X$ studied by
Kucharczyk and Scholze. For well behaved topological spaces, $\pi_K (X,x)$ is
the pro-algebraic completion of the ordinary fundamental group $\pi_1 (X,x)$.
  We obtain some structural results on $\pi_K (X,x)$ by studying
(pseudo-)torsors attached to its quotients. This approach uses ideas of Nori in
algebraic geometry and a result of Deligne on Tannakian categories. We also
calculate $\pi_K (X,x)$ for some generalized solenoids.

28
The categories of this paper are: alg-geom
6
The categories of this paper are: astro-ph
4
The categories of this paper are: cond-mat
19
The categories of this paper are: eess
27
The categories of this paper are: comp-gas
17
The categories of this paper are: q-fin
32
The categories of this paper are: atom-ph
31
The categories of this paper are: ao-sci
0
The categories of this paper are: hep-ph
3
The categories of this paper are: physics
9
The categories of this paper are: nlin
8
The categories of this paper are: hep-ex
35
The categories of this paper are: mtrl-th
26
The categories of this paper are: bayes-an
37
The categories of this paper are: supr-con
5
The categories of this paper are: gr-qc