Sergey
Fomin, U. of Michigan Cluster complexes of bordered surfaces |
To an oriented surface with boundary and finitely many marked points
one can associate a simplicial complex (indeed, a pseudomanifold),
namely, the cluster complex of the corresponding cluster algebra.
I will present a self-contained description of this complex in terms
of the combinatorial topology of [the triangulations of] the surface;
give examples, which include associahedra of types A and D; and state
some proven and conjectural properties of cluster complexes.
No background on cluster algebras is required. This is joint work
with Michael Shapiro and Dylan Thurston.