Artículos con la etiqueta ‘Geometría topologica’

Generalizations of the Kolmogorov-Barzdin embedding estimates

Por • 11 feb, 2014 • Category: Ciencia y tecnología

We consider several ways to measure the `geometric complexity’ of an embedding from a simplicial complex into Euclidean space. One of these is a version of `thickness’, based on a paper of Kolmogorov and Barzdin. We prove inequalities relating the thickness and the number of simplices in the simplicial complex, generalizing an estimate that Kolmogorov and Barzdin proved for graphs. We also consider the distortion of knots. We give an alternate proof of a theorem of Pardon that there are isotopy classes of knots requiring arbitrarily large distortion. This proof is based on the expander-like properties of arithmetic hyperbolic manifolds.

GLC actors, artificial chemical connectomes, topological issues and knots

Por • 25 dic, 2013 • Category: Educacion

Based on graphic lambda calculus, we propose a program for a new model of asynchronous distributed computing, inspired from Hewitt Actor Model, as well as several investigation paths, concerning how one may graft lambda calculus and knot diagrammatics.

Updates on Hirzebruch’s 1954 Problem List

Por • 23 may, 2013 • Category: Educacion

We present updates to the problems on Hirzebruch’s 1954 problem list focussing on open problems, and on those where substantial progress has been made in recent years. We discuss some purely topological problems, as well as geometric problems about (almost) complex structures, both algebraic and non-algebraic, about contact structures, and about (complementary pairs of) foliations.