The Hopf algebra of finite topologies and mould composition
[Algèbre de Hopf des topologies finies et composition moulienne]
Annales de l'Institut Fourier, Tome 67 (2017) no. 3, pp. 911-945.

Nous mettons en évidence un coproduit interne sur l’algèbre de Hopf des topologies finies introduite récemment par C. Malvenuto, F. Patras et le second auteur. Ce coproduit est dual de la composition des “quasi-ormoules”, version naturelle des moules, selon la terminologie de J. Ecalle, dans ce contexte.

We exhibit an internal coproduct on the Hopf algebra of finite topologies recently defined by the second author, C. Malvenuto and F. Patras, dual to the composition of “quasi-ormoulds”, which are the natural version of J. Ecalle’s moulds in this setting. All these results are displayed in the linear species formalism.

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DOI : 10.5802/aif.3100
Classification : 05E05, 06A11, 16T30
Keywords: finite topological spaces, Hopf algebras, mould calculus, posets, quasi-orders
Mot clés : espaces topologiques finis, algèbres de Hopf, calcul moulien, ensembles partiellement ordonnés, préordres
Fauvet, Frédéric 1 ; Foissy, Loïc 2 ; Manchon, Dominique 3

1 IRMA, 10 rue du Général Zimmer, 67084 Strasbourg Cedex (France)
2 Université du Littoral - Côte d’Opale 50 Rue Ferdinand Buisson 62100 Calais (France)
3 Université Blaise Pascal CNRS-UMR 6620 3 place Vasarély CS 60026 63178 Aubière (France)
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Fauvet, Frédéric; Foissy, Loïc; Manchon, Dominique. The Hopf algebra of finite topologies and mould composition. Annales de l'Institut Fourier, Tome 67 (2017) no. 3, pp. 911-945. doi : 10.5802/aif.3100. http://archive.numdam.org/articles/10.5802/aif.3100/

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