• Corpus ID: 117268858

Constructive Homological Algebra and Applications

@article{Rubio2012ConstructiveHA,
  title={Constructive Homological Algebra and Applications},
  author={Julio Rubio and Francis Sergeraert},
  journal={arXiv: K-Theory and Homology},
  year={2012}
}
This text was written and used for a MAP Summer School at the University of Genova, August 28 to September 2, 2006. Available since then on the web site of the second author, it has been used and referenced by several colleagues working in Commutative Algebra and Algebraic Topology. To make safer such references, it was suggested to place it on the Arxiv repository. It is a relatively detailed exposition of the use of the Basic Perturbation Lemma to make constructive Homological Algebra… 

Interoperating between computer algebra systems: computing homology of groups with kenzo and GAP

Once HAP output is integrated into Kenzo, it can be used to compute more complicated algebraic invariants such as the homology groups of various 2-types.

Verified computing in homological algebra

It is shown that Coq is not always up to its promises and that theoretical works will be necessary to understand how these limits can be relaxed.

Effective Computation of Generalized Spectral Sequences

Algorithms and programs for computing generalized spectral sequences, a useful tool in Computational Algebraic Topology which provides topological information on spaces with generalized filtrations over a poset are presented.

Combinatorial Koszul Homology: Computations and Applications

With a particular focus on explicit computations and applications of the Koszul homology and Betti numbers of monomial ideals, the main goals of this thesis are the following: Analyze the Koszul

An implementation of effective homotopy of fibrations

Computing the first stages of the Bousfield-Kan spectral sequence

  • A. Romero
  • Mathematics
    Applicable Algebra in Engineering, Communication and Computing
  • 2010
The algorithm to get the effective homology of RX from the effective Homological Algebra of X can be considered the main result, and a combinatorial proof of the convergence of the Bousfield-Kan spectral sequence, based on the tapered nature of the stage E1.

Effective homology and spectral sequences

Effective homology and spectral sequences are two different techniques of Algebraic Topology which can be used for the computation of homology and homotopy groups. In this work we try to relate both

A Bousfield–Kan Algorithm for Computing the Effective Homotopy of a Space

The constructive constraint of the BKSS leads to a significant reorganization of this rich material and, as it is most often the case, to a simpler and more explicit description.

Integration of the Kenzo System within SageMath for New Algebraic Topology Computations

This work makes it possible to communicate both computer algebra programs and the SageMath system with new capabilities in algebraic topology, such as the computation of homotopy groups and some kind of spectral sequences, dealing in particular with simplicial objects of an infinite nature.

Homotopy groups of suspended classifying spaces: An experimental approach

The goal of this work is to obtain a computer program calculating π∗(ΣK(G, 1)) for a general group G, which will allow one to obtain as particular computations some theoretical results of [11], and to develop 2010 Mathematics Subject Classification.
...

References

SHOWING 1-10 OF 60 REFERENCES

Constructive algebraic topology

The Rubio–Sergeraert solution for Constructive Algebraic Topology is recalled and the concrete computer program Kenzo has been written down which precisely follows this method.

A Singular Introduction to Commutative Algebra

From the reviews of the first edition: "It is certainly no exaggeration to say that A Singular Introduction to Commutative Algebra aims to lead a further stage in the computational revolution in

Algebraic models for homotopy types

The classical problem of algebraic models for homotopy types is precisely stated here in terms of our ability to compute with the models. Two dierent natural statements for this problem are produced,

Operads in algebra, topology, and physics

'Operads are powerful tools, and this is the book in which to read about them' - ""Bulletin of the London Mathematical Society"". Operads are mathematical devices that describe algebraic structures

Computing spectral sequences

A Concise Course in Algebraic Topology

Free resolutions and Koszul homology

Combinatorial operad actions on cochains

  • C. BergerB. Fresse
  • Mathematics
    Mathematical Proceedings of the Cambridge Philosophical Society
  • 2004
A classical E-infinity operad is formed by the bar construction of the symmetric groups. Such an operad has been introduced by M. Barratt and P. Eccles in the context of simplicial sets in order to

Computational Commutative Algebra 1

This is a book about Grbner bases and their applications. It contains 3 chapters, 20 sections, 44 tutorials, 165 exercises, and numerous further amusements. It is going to help you bridge the gap

A User’s Guide to Algebraic Topology

Preface. Introduction and Overview. 1. Basics of Extension and Lifting Problems. 2. Up to Homotopy is Good Enough. 3. Homotopy Group Theory. 4. Homology and Cohomology Theories. 5. Examples in
...