Programming before theorizing, a case study

  1. Romero, A. 1
  2. Sergeraert, F. 2
  1. 1 Universidad de La Rioja
    info

    Universidad de La Rioja

    Logroño, España

    ROR https://ror.org/0553yr311

  2. 2 Joseph Fourier University
    info

    Joseph Fourier University

    Grenoble, Francia

    ROR https://ror.org/02aj0kh94

Book:
Proceedings of the International Symposium on Symbolic and Algebraic Computation, ISSAC

ISBN: 9781450312691

Year of publication: 2012

Pages: 289-296

Type: Book chapter

DOI: 10.1145/2442829.2442871 SCOPUS: 2-s2.0-84874970125 GOOGLE SCHOLAR lock_openOpen access editor

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Abstract

This paper relates how a "simple" result in combinatorial homotopy eventually led to a totally new understanding of basic theorems in Algebraic Topology, namely the Eilenberg- Zilber theorem, the twisted Eilenberg-Zilber theorem, and finally the Eilenberg-MacLane correspondance between the Classifying Space and Bar constructions. In the last case, it was an amazing lucky consequence of computations based on conjectures not yet proved. The key new tool used in this context is Robin Forman's Discrete Vector Fields theory. Copyright 2012 ACM.