Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Homotopies and transcendental extensions in colouring problems   We develop the technique of geometric realizations with algebraically
independent (over the field of real algebraic numbers) coordinates of vertices
and combine it with the oriented volume method inspired by work of McLennan and
Tourky on the Sperner's lemma. This enables us to prove new results: the
non-draw property of the generalized Y~game, the theorem about triangulation of
the product of two simplices, the generalized Atanassov conjecture, and give
new proofs of known results: the multilabeled versions of Sperner's and Ky
Fan's lemmas.

14
The categories of this paper are: math-ph
4
The categories of this paper are: cond-mat
24
The categories of this paper are: dg-ga
31
The categories of this paper are: ao-sci
5
The categories of this paper are: gr-qc
34
The categories of this paper are: chem-ph
21
The categories of this paper are: adap-org
10
The categories of this paper are: q-bio
19
The categories of this paper are: eess
26
The categories of this paper are: bayes-an
9
The categories of this paper are: nlin
35
The categories of this paper are: mtrl-th
17
The categories of this paper are: q-fin
8
The categories of this paper are: hep-ex
12
The categories of this paper are: nucl-th
28
The categories of this paper are: alg-geom