Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Universal tree-graded spaces and asymptotic cones   We define and give explicit construction of the universal tree-graded space
with a given collection of pieces. We apply that to proving uniqueness of
asymptotic cones of relatively hyperbolic groups whose peripheral subgroups
have unique asymptotic cones. Modulo the Continuum Hypothesis, we show that if
an asymptotic cone of a geodesic metric space is homogeneous and has cut
points, then it is the universal tree-graded space with pieces - maximal
connected subsets without their own cut points. Thus it is completely
determined by its collection of pieces.

21
The categories of this paper are: adap-org
15
The categories of this paper are: nucl-ex
4
The categories of this paper are: cond-mat
20
The categories of this paper are: acc-phys
19
The categories of this paper are: eess
26
The categories of this paper are: bayes-an
37
The categories of this paper are: supr-con
1
The categories of this paper are: cs
29
The categories of this paper are: funct-an
13
The categories of this paper are: quant-ph
7
The categories of this paper are: hep-th
8
The categories of this paper are: hep-ex
36
The categories of this paper are: cmp-lg
28
The categories of this paper are: alg-geom
24
The categories of this paper are: dg-ga
11
The categories of this paper are: hep-lat