An implementation of effective homotopy of fibrations. (September 2019)

• Record Type: Journal Article
• Authors: Romero, Ana; Rubio, Julio; Sergeraert, Francis
• Is Part Of: Journal of symbolic computation. Volume 94(2019)
• Page Start: 149
• Page End: 172
• Publication Date: 2019-09
• Subjects: Constructive algebraic topology -- Effective homotopy -- Fibrations -- Homotopy groups -- Serre exact sequence -- Finitely generated groups -- Central extensions -- Setoid groups -- Effective setoid groups; Mathematics -- Data processing -- Periodicals; Numerical analysis -- Data processing -- Periodicals; Automatic programming (Computer science) -- Periodicals; Mathématiques -- Informatique -- Périodiques; Analyse numérique -- Informatique -- Périodiques; Programmation automatique -- Périodiques; Automatic programming (Computer science); Mathematics -- Data processing; Numerical analysis -- Data processing; Periodicals; Electronic journals; 510.285
• DOI: 10.1016/j.jsc.2018.08.001
• Languages: English
• ISSNs: 0747-7171

Abstract

Abstract: In this paper, we present a new module for the Kenzo system which makes it possible to compute the effective homotopy of the total space of a fibration, using the well-known long exact sequence of homotopy of a fibration defined by Jean-Pierre Serre. The programs are written in Common Lisp and require the implementation of new classes and functions corresponding to the definitions of setoid group (SG) and effective setoid group (ESG) . Moreover, we have included a new module for working with finitely generated abelian groups, choosing the representation of a free presentation by means of a matrix in canonical form. These tools are then used to implement the long exact homotopy sequence of a fibration. We illustrate with examples some applications of our results.