A Combinatorial Tool for Computing the Effective Homotopy of Iterated Loop Spaces

  1. Romero, A. 2
  2. Sergeraert, F. 1
  1. 1 Joseph Fourier University
    info

    Joseph Fourier University

    Grenoble, Francia

    ROR https://ror.org/02aj0kh94

  2. 2 Universidad de La Rioja
    info

    Universidad de La Rioja

    Logroño, España

    ROR https://ror.org/0553yr311

Journal:
Discrete and Computational Geometry

ISSN: 0179-5376

Year of publication: 2015

Volume: 53

Issue: 1

Pages: 1-15

Type: Article

DOI: 10.1007/S00454-014-9650-1 SCOPUS: 2-s2.0-84920074410 GOOGLE SCHOLAR

More publications in: Discrete and Computational Geometry

Institutional repository: lockOpen access Editor

Abstract

This paper is devoted to the Cradle Theorem. It is a recursive description of a discrete vector field on the direct product of simplices Δp × Δq endowed with the standard triangulation. The vector field provides an explicit deformation that is used to establish an algorithm for computing the Bousfield–Kan spectral sequence, more precisely to compute the homotopy groups (Formula presented) for G a 1-reduced simplicial abelian group.