Geodesic
The diagonal of cellular spaces and effective algebro-homotopical constructions
Anibal M. Medina-Mardones1
1Western University, London, Canada
EMS surveys in mathematical sciences, Tome 10 (2023) no. 2, pp. 223-241

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DOI

In this survey article we discuss certain homotopy coherent enhancements 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 has found applications in various fields including deformation theory, higher category theory, and condensed matter physics.
DOI : 10.4171/emss/71
Classification : 55-XX, 18-XX
Mots-clés : cellular chains, diagonal map, effective constructions, C∞​-coalgebras, E∞​-coalgebras

Anibal M. Medina-Mardones  1

1 Western University, London, Canada 
Anibal M. Medina-Mardones. The diagonal of cellular spaces and effective algebro-homotopical constructions. EMS surveys in mathematical sciences, Tome 10 (2023) no. 2, pp. 223-241. doi: 10.4171/emss/71
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