Michael W. Davis, Tadeusz Januszkiewicz, and Richard Scott, Nonpositive curvature of blow-ups, Sel. Math., New Ser. 4 (1998), no. 4, 491-547. 17 Home/Search Document Details and Download
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Geometry of the Space of Phylogenetic Trees - Billera, Holmes, Vogtmann (1999) (3 citations) (Correct)
....1 2 3 4 0 1 2 3 4 Figure 3: Associahedron in the case n =4 By gluing associahedra together, one can construct a space of planar labeled trees with n leaves, where each associahedron corresponds to a different ordering of the labels. This space has appeared in several di#erent contexts (Davis et al. 1998; Devadoss, 1999; Kapranov, 1993) and is denoted M 0,n 1 . The space M 0,5 is tiled with 12 pentagons, corresponding to all possible permutations of the leaves up to complete reversal. Each space M 0,n 1 has a dual tiling by (n 3) dimensional cubes. The dual tiling of M 0,5 , by squares, is ....
....at P and at all vertices below P produces an equivalent tree. The manifold M 0,n 1 has been studied by mathematicians in a variety of di#erent guises (moduli space of stable (n 1) pointed curves, minimal blow up of the projective braid arrangement, cyclic operad of mosaics) See for example Davis et al. 1998); Devadoss (1999) Kapranov (1993) the latter especially gives some background references. 3.2. Combinatorics of the link of the origin An alternate description of the link L n can be given in terms of partitions of the set 0, 1, n of leaves (recall that we have attached a leaf labeled 0 ....
M. Davis, T. Januszkiewicz, and R. Scott. Nonpositive curvature of blowups. Selecta Math. (New Series), 4(4):491--547, 1998.
On Groups Acting On Nonpositively Curved Cubical Complexes - Ballmann, Swiatkowski (Correct)
....arise naturally from many constructions. Among them are graph products of groups and other groups acting on right angled buildings, fundamental groups of hyperbolizations of polyhedra, of toric manifolds and of blow ups of arrangements of hyperplanes, and many others (see [Da] DJ1] DJ2] [DJS] and Section 2 below) Roughly speaking, a cubical complex is a cell complex whose cells are cubes. As a definition of nonpositive curvature we use the comparison triangle condition CAT(0) with respect to the natural cubical metric of a cubical complex (see Section 1 below for more details) It ....
....1 and 2 of the introduction. The universal cover of h j (K) is hyperbolic in many cases, but not always, see [Gr] CD] Zonotopal Complexes In this subsection we briefly describe an extended class of cell complexes to which the Mobius band hyperbolization procedure can be applied, see [DJS] for more details. Recall that the product with interval procedure applies to all cell complexes. An arrangement in a real vector space V is a finite collection H of linear subspaces of V with codimension one. Elements of H are called hyperplanes. An arrangement H is essential if the ....
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M. Davis, T. Januszkiewicz, P. Scott, Nonpositive curvature of blow-ups, preprint, 1997.
Projectivities in Simplicial Complexes and Colorings of Simple.. - Joswig (2001) (1 citation) (Correct)
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Michael W. Davis, Tadeusz Januszkiewicz, and Richard Scott, Nonpositive curvature of blow-ups, Sel. Math., New Ser. 4 (1998), no. 4, 491-547. 17
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