Geodesic
Non-Kissing Complexes for Gentle Algebras
Séminaire lotharingien de combinatoire, 80B (2018)
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We introduce the non-kissing complex of any gentle bound quiver. This complex provides a powerful combinatorial model for support τ-tilting theory over gentle algebras, and it generalizes and unifies the previously considered situations of quivers defined from subsets of the grid or from dissections of a polygon (both generalizing the classical associahedron). In this extended abstract, we report on lattice theoretic and geometric properties of finite non-kissing complexes: we show that their flip graphs are Hasse diagrams of congruence-uniform lattices, and that they can be realized by convex polytopes. 

@article{SLC_2018_80B_a38,
     author = {Yann Palu and Vincent Pilaud and Pierre-Guy Plamondon},
     title = {Non-Kissing {Complexes} for {Gentle} {Algebras}},
     journal = {S\'eminaire lotharingien de combinatoire},
     year = {2018},
     volume = {80B},
     url = {http://geodesic.mathdoc.fr/item/SLC_2018_80B_a38/}
}
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AU  - Yann Palu
AU  - Vincent Pilaud
AU  - Pierre-Guy Plamondon
TI  - Non-Kissing Complexes for Gentle Algebras
JO  - Séminaire lotharingien de combinatoire
PY  - 2018
VL  - 80B
UR  - http://geodesic.mathdoc.fr/item/SLC_2018_80B_a38/
ID  - SLC_2018_80B_a38
ER  - 
%0 Journal Article
%A Yann Palu
%A Vincent Pilaud
%A Pierre-Guy Plamondon
%T Non-Kissing Complexes for Gentle Algebras
%J Séminaire lotharingien de combinatoire
%D 2018
%V 80B
%U http://geodesic.mathdoc.fr/item/SLC_2018_80B_a38/
%F SLC_2018_80B_a38
Yann Palu; Vincent Pilaud; Pierre-Guy Plamondon. Non-Kissing Complexes for Gentle Algebras. Séminaire lotharingien de combinatoire, 80B (2018). http://geodesic.mathdoc.fr/item/SLC_2018_80B_a38/