In this paper, we prove various results concerning DGA-algebras in the context of the
Homological Perturbation Theory. We distinguish two class of contractions for algebras: full …

The Cartan formula encodes the relationship between the cup product and the action of the
Steenrod algebra in F p-cohomology. In this work, we present an effective proof of the …

John McCleary insisted in his interesting textbook entitled “User's guide to spectral
sequences” on the fact that the tool “spectral sequence” is not in the general situation an …

We present here a combinatorial method for computing Steenrod squares of a simplicial set
X. This method is essentially based on the determination of explicit formulae for the …

This book gives a thorough introduction to topological data analysis (TDA), the application of
algebraic topology to data science. Algebraic topology is traditionally a very specialized field …

In a previous paper we characterized, in the Category Theory setting, a class of
implementations of Abstract Data Types, which has been suggested by the way of …

Abstract The Eilenberg–Zilber algorithm is one of the central components of the computer
algebra system called Kenzo, devoted to computing in Algebraic Topology. In this article we …

Working in a simplicial and constructive context, a new spectral system is defined that
relates Serre and Eilenberg–Moore spectral sequences associated to a principal simplicial …

We show that Szczarba's twisting cochain for a twisted Cartesian product is essentially the
same as the one constructed by Shih. More precisely, Szczarba's twisting cochain can be …

We construct an $ A_\infty $-structure on the two-sided bar construction involving homotopy
Gerstenhaber algebras (hgas). It extends the non-associative product defined by Carlson …