A Combinatorial Tool for Computing the Effective Homotopy of Iterated Loop Spaces
- Romero, A. 2
- Sergeraert, F. 1
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1
Joseph Fourier University
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2
Universidad de La Rioja
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ISSN: 0179-5376
Year of publication: 2015
Volume: 53
Issue: 1
Pages: 1-15
Type: Article
More publications in: Discrete and Computational Geometry
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.