Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A bijection between $m$-cluster-tilting objects and $(m+2)$-angulations
  in $m$-cluster categories   In this article, we study the geometric realizations of $m$-cluster
categories of Dynkin types A, D, $\tilde{A}$ and $\tilde{D}$. We show, in those
four cases, that there is a bijection between $(m+2)$-angulations and
isoclasses of basic $m$-cluster tilting objects. Under these bijections, flips
of $(m+2)$-angulations correspond to mutations of $m$-cluster tilting objects.
Our strategy consists in showing that certain Iyama-Yoshino reductions of the
$m$-cluster categories under consideration can be described in terms of cutting
along an arc the corresponding geometric realizations. This allows to infer
results from small cases to the general ones.

19
The categories of this paper are: eess
31
The categories of this paper are: ao-sci
17
The categories of this paper are: q-fin
4
The categories of this paper are: cond-mat
23
The categories of this paper are: solv-int
24
The categories of this paper are: dg-ga
30
The categories of this paper are: q-alg
36
The categories of this paper are: cmp-lg
35
The categories of this paper are: mtrl-th
20
The categories of this paper are: acc-phys
22
The categories of this paper are: chao-dyn
32
The categories of this paper are: atom-ph
37
The categories of this paper are: supr-con
6
The categories of this paper are: astro-ph
0
The categories of this paper are: hep-ph
28
The categories of this paper are: alg-geom