• Corpus ID: 243985985

The diagonal of cellular spaces and effective algebro-homotopical constructions

@inproceedings{MedinaMardones2021TheDO,
  title={The diagonal of cellular spaces and effective algebro-homotopical constructions},
  author={Anibal M. Medina-Mardones},
  year={2021}
}
. In this survey article we discuss certain homotopy coherent en- hancements of the coalgebra structure on cellular chains defined by an approximation to the diagonal. Over the rational numbers, C ∞ -coalgebra structures control the Q -complete homotopy theory of spaces, and over the integers, E ∞ coalgebras provide an appropriate setting to model the full homotopy category. Effective constructions of these structures, the focus of this work, carry geometric and combinatorial information which… 

Figures from this paper

References

SHOWING 1-10 OF 54 REFERENCES
A general algebraic approach to steenrod operations
The cobar construction as an $E_{\infty}$-bialgebra model of the based loop space
In the fifties, Adams introduced a comparison map θZ : ΩS (Z, z) → S (Ωz Z) from his cobar construction on the (simplicial) singular chains of a pointed space (Z, z) to the cubical singular chains on
On the multisimplicial cup product
We define a cup product on the cochain complex of a multisimplicial set, that is compatible with the classical cup product on the cochain complex of the diagonal simplicial set via the
Cochain level May–Steenrod operations
Abstract Steenrod defined in 1947 the Steenrod squares on the mod 2 cohomology of spaces using explicit cochain formulae for the cup-i products; a family of coherent homotopies derived from the
A cochain level proof of Adem relations in the mod 2 Steenrod algebra
In 1947, N.E. Steenrod defined the Steenrod Squares, which are mod 2 cohomology operations, using explicit cochain formulae for cup-i products of cocycles. He later recast the construction in more
Explicit symmetric DGLA models of 3-cells
Abstract We give explicit formulae for differential graded Lie algebra (DGLA) models of $3$ -cells. In particular, for a cube and an $n$ -faceted banana-shaped $3$ -cell with two vertices, $n$
An algebraic representation of globular sets
We describe a fully faithful embedding of the category of (reflexive) globular sets into the category of counital cosymmetric $R$-coalgebras when $R$ is an integral domain. This embedding is a lift
Moscow 1935: Topology Moving Toward America
The International Conference in Topology in Moscow, September 4–10, 1935, was notable in several ways. To start, it was the first truly international conference in a specialized part of mathematics,
...
...