40 research outputs found
Coxeter Complexes and Graph-Associahedra
Given a graph G, we construct a simple, convex polytope whose face poset is
based on the connected subgraphs of G. This provides a natural generalization
of the Stasheff associahedron and the Bott-Taubes cyclohedron. Moreover, we
show that for any simplicial Coxeter system, the minimal blow-ups of its
associated Coxeter complex has a tiling by graph-associahedra. The geometric
and combinatorial properties of the complex as well as of the polyhedra are
given. These spaces are natural generalizations of the Deligne-Knudsen-Mumford
compactification of the real moduli space of curves.Comment: 18 pages, 9 figures; revised content and reference
Diagonalizing the genome II: toward possible applications
In a previous paper, we showed that the orientable cover of the moduli space
of real genus zero algebraic curves with marked points is a compact aspherical
manifold tiled by associahedra, which resolves the singularities of the space
of phylogenetic trees. In this draft of a sequel, we construct a related
(stacky) resolution of a space of real quadratic forms, and suggest, perhaps
without much justification, that systems of oscillators parametrized by such
objects may may provide useful models in genomics.Comment: 11 pages, 3 figure