Overview.

     The Kenzo program implements the methods of Constructive Algebraic Topology. The funny corresponding acronym CAT gave the idea to name this program as my beloved cat.

     The first version of this program, called EAT for Effective Algebraic Topology, was a joint work with Julio Rubio (1990). The EAT program was totally rewritten with Xavier Dousson in 1998, becoming Kenzo, on the one hand to include many technical improvements, in particular in memory management, improvements deduced from the EAT experience, and on the other hand to implement the Whitehead Tower and compute homotopy groups of arbitrary simply connected simplicial sets, the heart of Xavier's thesis. A detailed Kenzo documentation was simulatneously written by Yvon Siret.

     The 1.1.8 version now proposed takes account of the new mathematical technology based on Discrete Vector Fields. Discovered by Robin Forman, it happens this method considerably improves the implementation of the Eilenberg-Zilber theorem, twisted or not, and also the computation of the effective homology of the Eilenberg-MacLane spaces, crucial when using the Postnikov or Whitehead towers.


Examples of results obtained thanks to the Kenzo program.

Other examples of results reachable by Kenzo:


Kenzo extensions.

A Kenzo extension deserves to be signalled: written by Ana Romero, it gives a complete description of the Serre and Eilenberg-Moore spectral sequences when versions with homology effective are known for the initial spaces. See Ana Romero's paper, now published in JSC.

Ana Romero also wrote various new Kenzo-modules devoted to some methods allowing her to compute the effective homology of some groups and so to obtain for example the first homotopy groups πkSBG for some simple non-commutative groups G. Work in progress.

You can be interested by this small Kenzo-demonstration file.

See also the Barcelona demonstration given in the 3rd European Congress of Mathematics.


The detailed Kenzo documentation (340 p.) was written by Yvon Siret in 1998-9. Yvon Siret was not a topologist, he was "only" (?!) a (very good) computer scientist, who learned Algebraic Topology when writing this document. His advices were also often crucial when writing down the source code. Many thanks to him!


Updated Kenzo-Source (Version 1-1-7, October 11, 2008)

     Previous various compressed archives (tgz, tar and zip) have been replaced by this unique 7zip version, usable under Linux and Windows as well, much more compact! In particular, the previous Kenzo-doc.pdf component, non-searchable, has been replaced by another equal (!) version available elsewhere, searchable. Thanks to Marek Kaluba for the notification.


EAT (= Effective Algebraic Topology), the previous program.

Before the Kenzo program (1998), the EAT program was written in 1990 by Julio Rubio and FS. It was the first program ever written implementing spectral sequences, in fact only some particular cases of the Eilenberg-Moore spectral sequence. The goal was the computation of the first homology groups of some loop spaces, for which no algorithm was previously concretely available. An implementation rather primitive, just designed to illustrate our methods of Effective Homology by a concrete experimental program.

The EAT program is also studied by logicians and computer scientists. Those possibly interested can download the EAT-program and its documentation.