Concept
Cap product
Related publications (6)
Cochains are all you need
In this thesis, we apply cochain complexes as an algebraic model of space in a diverse range of mathematical and scientific settings. We begin with an algebraic-discrete Morse theory model of auto-encoding cochain data, connecting the homotopy theory of d ...
EPFL2024An effective proof of the Cartan formula: The even prime
Anibal Maximiliano Medina Mardones
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 Cartan formula at the cochain level when the field is F-2. More explicitly, for ...
2020Hochschild (co)homology of Koszul dual pairs
In this article we prove that the Tamarkin–Tsygan calculus of an Adams connected augmented dg algebra and of its Koszul dual are dual to each other. This uses the fact that the Hochschild cohomology and homology may be regarded as a twisted convolution dg ...
2019The cup product of Brooks quasimorphisms
We prove the vanishing of the cup product of the bounded cohomology classes associated to any two Brooks quasimorphisms on the free group. This is a consequence of the vanishing of the square of a universal class for tree automorphism groups. ...
WALTER DE GRUYTER GMBH2018Using torsion theory to compute the algebraic structure of Hochschild (co)homology
The aim of this article is to provide explicit formulas for the cup product on the Hochschild cohomology of any nonnegatively graded connected algebra and for the cap products on the Hochschild homology of with coefficients in any graded bimodule at the le ...
2018A higher homotopic extension of persistent (co)homology
Our objective is to show a possibly interesting structure of homotopic nature appearing in persistent (co)homology. Assuming that the filtration of a simplicial set embedded in induces a multiplicative filtration on the dg algebra of simplicial cochains, w ...
2018