Non-kissing complexes and tau-tilting for gentle algebras

By Yann Palu, Vincent Pilaud, Pierre-Guy Plamondon. Memoirs of the American Mathematical Society, 2017

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We interpret the support τ \tau -tilting complex of any gentle bound quiver as the non-kissing complex of walks on its blossoming quiver. Particularly relevant examples were previously studied for quivers defined by a subset of the grid or by a dissection of a polygon. We then focus on the case when the non-kissing complex is finite. We show that the graph of increasing flips on its facets is the Hasse diagram of a congruence-uniform lattice. Finally, we study its g \mathbf {g} -vector fan and prove that it is the normal fan of a non-kissing associahedron.

Subfields: Atomic and Molecular Physics, and Optics, Discrete Mathematics and Combinatorics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/681b2d05c5f6126455c20b1338ab9abc846bfcf9