Search results for "simplicial"

Automorphisms of simplicial complexes and their Stanley-Reisner rings

1997

On the proper homotopy invariance of the Tucker property

2006

A non-compact polyhedron P is Tucker if, for any compact subset K ⊂ P, the fundamental group π1(P − K) is finitely generated. The main result of this note is that a manifold which is proper homotopy equivalent to a Tucker polyhedron is Tucker. We use Poenaru’s theory of the equivalence relations forced by the singularities of a non-degenerate simplicial map.

Online Edge Flow Imputation on Networks

2022

Author's accepted manuscript © 2022 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works. An online algorithm for missing data imputation for networks with signals defined on the edges is presented. Leveraging the prior knowledge intrinsic to real-world networks, we propose a bi-level optimization scheme that exploits the causal dependencies and the flow conservation, respe…

Z2-Regge versus standard Regge calculus in two dimensions

1999

We consider two versions of quantum Regge calculus: the standard Regge calculus where the quadratic link lengths of the simplicial manifold vary continuously and the ${Z}_{2}$ Regge model where they are restricted to two possible values. The goal is to determine whether the computationally more easily accessible ${Z}_{2}$ model still retains the universal characteristics of standard Regge theory in two dimensions. In order to compare observables such as the average curvature or Liouville field susceptibility, we use in both models the same functional integration measure, which is chosen to render the ${Z}_{2}$ Regge model particularly simple. Expectation values are computed numerically and …

A star product in lattice gauge theory

1993

Abstract We consider a variant of the cup product of simplicial cochains and its applications in discrete formulations of non-abelian gauge theory. The standard geometrical ingredients in the continuum theory all have natural analogues on a simplicial complex when this star product is used to translate the wedge product of differential forms. Although the star product is non-associative, it is graded-commutative, and the coboundary operator acts as a deviation on the star algebra. As such, it is reminiscent of the star product considered in some approaches to closed string field theory, and we discuss applications to the three dimensional non-abelian Chern-Simons theory.

Constraints on Area Variables in Regge Calculus

2000

We describe a general method of obtaining the constraints between area variables in one approach to area Regge calculus, and illustrate it with a simple example. The simplicial complex is the simplest tessellation of the 4-sphere. The number of independent constraints on the variations of the triangle areas is shown to equal the difference between the numbers of triangles and edges, and a general method of choosing independent constraints is described. The constraints chosen by using our method are shown to imply the Regge equations of motion in our example.

Weighted limits in simplicial homotopy theory

2010

Abstract By combining ideas of homotopical algebra and of enriched category theory, we explain how two classical formulas for homotopy colimits, one arising from the work of Quillen and one arising from the work of Bousfield and Kan, are instances of general formulas for the derived functor of the weighted colimit functor.

A criterion for homeomorphism between closed Haken manifolds

2003

In this paper we consider two connected closed Haken manifolds denoted by M^3 and N^3, with the same Gromov simplicial volume. We give a simple homological criterion to decide when a given map f: M^3-->N^3 between M^3 and N^3 can be changed by a homotopy to a homeomorphism. We then give a convenient process for constructing maps between M^3 and N^3 satisfying the homological hypothesis of the map f.

Moment-angle complexes and complexe manifolds

2010

The aim of this thesis is to extend the results of the article [B-M] on the relations between moment-angle complexes and complex manifolds. We will focus here on moment-angle complexes defined by a simplicial (not only polytopal) decomposition of the sphere. We will also seek to use the relationship between these two kinds of objects to be understand the topology of several complex manifolds. [B-M] F.Bosio, L.Meersseman, Real quadrics in Cn, complex manifolds and polytopes, Acta Mathematica, 197 (2006), n° 1, 53 -- 127.

Homologia simplicial i la seua aplicació a l'anàlisi musical

2018

En topologia, l’homologia és una ferramenta molt útil que ens permet diferenciar entre distints espais topològics. La idea és associar a cada espai un grup en cada dimensió n, anomenat n-èsim grup d’homologia de X que, intuïtivament, mesura els “forats n-dimensionals” de l’espai. Existeixen diverses teories d’homologia que s’apliquen a diferents classes d’espais. En aquest treball presentarem una de les més senzilles i intuïtives: l’homologia simplicial. L’objectiu és que aquest text puga servir d’introducció a la matèria, i per tant ha sigut escrit amb la idea que siga comprensible sense més requisits que haver cursat l’assignatura de Topologia del Grau de Matemàtiques. Al primer capítol e…