2,993 research outputs found
Braids, posets and orthoschemes
In this article we study the curvature properties of the order complex of a
graded poset under a metric that we call the ``orthoscheme metric''. In
addition to other results, we characterize which rank 4 posets have CAT(0)
orthoscheme complexes and by applying this theorem to standard posets and
complexes associated with four-generator Artin groups, we are able to show that
the 5-string braid group is the fundamental group of a compact nonpositively
curved space.Comment: 33 pages, 16 figure
Image = Structure + Few Colors
Topology plays an important role in computer vision by capturing
the structure of the objects. Nevertheless, its potential applications
have not been sufficiently developed yet. In this paper, we combine the
topological properties of an image with hierarchical approaches to build a
topology preserving irregular image pyramid (TIIP). The TIIP algorithm
uses combinatorial maps as data structure which implicitly capture the
structure of the image in terms of the critical points. Thus, we can achieve
a compact representation of an image, preserving the structure and topology
of its critical points (maxima, the minima and the saddles). The parallel
algorithmic complexity of building the pyramid is O(log d) where d is
the diameter of the largest object.We achieve promising results for image
reconstruction using only a few color values and the structure of the image,
although preserving fine details including the texture of the image
Fields of moduli of three-point G-covers with cyclic p-Sylow, I
We examine in detail the stable reduction of Galois covers of the projective
line over a complete discrete valuation field of mixed characteristic (0, p),
where G has a cyclic p-Sylow subgroup of order p^n. If G is further assumed to
be p-solvable (i.e., G has no nonabelian simple composition factors with order
divisible by p), we obtain the following consequence: Suppose f: Y --> P^1 is a
three-point G-Galois cover defined over the complex numbers. Then the nth
higher ramification groups above p for the upper numbering of the (Galois
closure of the) extension K/Q vanish, where K is the field of moduli of f. This
extends work of Beckmann and Wewers. Additionally, we completely describe the
stable model of a general three-point Z/p^n-cover, where p > 2.Comment: Major reorganization. In particular, the former Appendix C has been
spun off and is now arxiv:1109.4776. Now 42 page
Steinitz Theorems for Orthogonal Polyhedra
We define a simple orthogonal polyhedron to be a three-dimensional polyhedron
with the topology of a sphere in which three mutually-perpendicular edges meet
at each vertex. By analogy to Steinitz's theorem characterizing the graphs of
convex polyhedra, we find graph-theoretic characterizations of three classes of
simple orthogonal polyhedra: corner polyhedra, which can be drawn by isometric
projection in the plane with only one hidden vertex, xyz polyhedra, in which
each axis-parallel line through a vertex contains exactly one other vertex, and
arbitrary simple orthogonal polyhedra. In particular, the graphs of xyz
polyhedra are exactly the bipartite cubic polyhedral graphs, and every
bipartite cubic polyhedral graph with a 4-connected dual graph is the graph of
a corner polyhedron. Based on our characterizations we find efficient
algorithms for constructing orthogonal polyhedra from their graphs.Comment: 48 pages, 31 figure
- …