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Concept

Ensemble simplicial

Publications associées (32)

On Simplices in Diameter Graphs in R-4

Andrei Kupavskii

A graph G is a diameter graph in R-d if its vertex set is a finite subset in R-d of diameter 1 and edges join pairs of vertices a unit distance apart. It is shown that if a diameter graph G in R-4 contains the complete subgraph K on five vertices, then any ...

Maik Nauka/Interperiodica/Springer2017

High order discontinuous Galerkin methods on simplicial elements for the elastodynamics equation

Alfio Quarteroni

In this work we apply the discontinuous Galekin (dG) spectral element method on meshes made of simplicial elements for the approximation of the elastodynamics equation. Our approach combines the high accuracy of spectral methods, the geometrical flexibilit ...

Springer Verlag2016

Waldhausen K-theory of spaces via comodules

Kathryn Hess Bellwald

Let X be a simplicial set. We construct a novel adjunction be- tween the categories RX of retractive spaces over X and ComodX+ of X+- comodules, then apply recent work on left-induced model category structures [5], [16] to establish the existence of a left ...

Academic Press Inc Elsevier Science2016

Kan spectra, group spectra and twisting structures

Marc Stephan

Kan spectra provide a combinatorial model for the stable homotopy category. They were introduced by Dan Kan in 1963 under the name semisimplicial spectra. A Kan spectrum is similar to a pointed simplicial set, but it has simplices in negative degrees as we ...

EPFL2015

Remarks on Schur's conjecture

János Pach, Filip Moric

Let P be a set of n > d points in for d >= 2. It was conjectured by Zvi Schur that the maximum number of (d-1)-dimensional regular simplices of edge length diam(P), whose every vertex belongs to P, is n. We prove this statement under the condition that any ...

Elsevier Science Bv2015

Bounds for Pach's Selection Theorem and for the Minimum Solid Angle in a Simplex

Jan Kyncl

We estimate the selection constant in the following geometric selection theorem by Pach: For every positive integer d, there is a constant such that whenever are n-element subsets of , we can find a point and subsets for every , each of size at least , suc ...

Springer2015

Extendability of Continuous Maps Is Undecidable

We consider two basic problems of algebraic topology: the extension problem and the computation of higher homotopy groups, from the point of view of computability and computational complexity. The extension problem is the following: Given topological space ...

Springer2014

Polynomial-Time Computation Of Homotopy Groups And Postnikov Systems In Fixed Dimension

For several computational problems in homotopy theory, we obtain algorithms with running time polynomial in the input size. In particular, for every fixed k >= 2, there is a polynomial-time algorithm that, for a 1-connected topological space X given as a f ...

Siam Publications2014

On The Image Of The Almost Strict Morse N-Category Under Almost Strict N-Functors

In an earlier work, we constructed the almost strict Morse n-category X which extends Cohen Sz Jones Sz Segal's flow category. In this article, we define two other almost strict n-categories V and W where V is based on homomorphisms between real vector spa ...

Mount Allison University2014

Homotopy completion and topological Quillen homology of structured ring spectra

Kathryn Hess Bellwald

Working in the context of symmetric spectra, we describe and study a homotopy completion tower for algebras and left modules over operads in the category of modules over a commutative ring spectrum (eg structured ring spectra). We prove a strong convergenc ...

Geometry & Topology Publications2013

Comments on: Recent progress on the combinatorial diameter of polytopes and simplicial complexes

Friedrich Eisenbrand

This paper features two main contributions. On the one hand, it gives an impressive survey on the progress on the diameter problem, including the breakthrough of the author with his disproof of the Hirsch conjecture among many other recent results. On the ...

Springer2013

Two and a half billion years of distance research

János Pach, Filip Moric

In a seminal paper published in 1946, Erd ̋os initiated the investigation of the distribution of distances generated by point sets in metric spaces. In spite of some spectacular par- tial successes and persistent attacks by generations of mathe- maticians, ...

2013

Publications associées (32)