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"We interpret the support -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-vector fan and prove that it is the normal fan of a non-kissing associahedron"--

Combinatorial analysis. --- Representations of algebras. --- Partially ordered sets. --- Congruence lattices. --- Convex polytopes. --- Associative rings and algebras -- Representation theory of rings and algebras -- Representations of Artinian rings. --- Associative rings and algebras -- Representation theory of rings and algebras -- Representations of quivers and partially ordered sets. --- Combinatorics -- Algebraic combinatorics -- Combinatorial aspects of representation theory. --- Combinatorics -- Algebraic combinatorics -- Combinatorial aspects of simplicial complexes. --- Order, lattices, ordered algebraic structures -- Lattices -- Ideals, congruence relations. --- Convex and discrete geometry -- Polytopes and polyhedra -- $n$-dimensional polytopes.