Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Exchange graphs and Ext quivers   We study the oriented exchange graph $\textrm{EG}^\circ(\Gamma_{N}\,Q)$ of
reachable hearts in the finite-dimensional derived category
$\mathcal{D}(\Gamma_{N}\,Q)$ of the CY-$N$ Ginzburg algebra $\Gamma_{N}Q$
associated to an acyclic quiver $Q$. We show that any such heart is induced
from some heart in the bounded derived category $\mathcal{D}(Q)$ via some
`Lagrangian immersion'
$\mathcal{L}:\mathcal{D}(Q)\to\mathcal{D}(\Gamma_{N}\,Q)$. We build on this to
show that the quotient of $\textrm{EG}^\circ(\Gamma_{N}\,Q)$ by the
Seidel-Thomas braid group is the exchange graph $\textrm{CEG}_{N-1}(Q)$ of
cluster tilting sets in the (higher) cluster category $\mathcal{C}_{N-1}(Q)$.
As an application, we interpret Buan-Thomas' coloured quiver for a cluster
tilting set in terms of the Ext quiver of any corresponding heart in
$\mathcal{D}(\Gamma_{N}\,Q)$.

30
The categories of this paper are: q-alg
9
The categories of this paper are: nlin
16
The categories of this paper are: stat
31
The categories of this paper are: ao-sci
13
The categories of this paper are: quant-ph
33
The categories of this paper are: plasm-ph
25
The categories of this paper are: patt-sol
11
The categories of this paper are: hep-lat
5
The categories of this paper are: gr-qc
23
The categories of this paper are: solv-int
27
The categories of this paper are: comp-gas
0
The categories of this paper are: hep-ph
32
The categories of this paper are: atom-ph
3
The categories of this paper are: physics
12
The categories of this paper are: nucl-th
10
The categories of this paper are: q-bio