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Reconnectads
Dotsenko, Vladimir1; Keilthy, Adam2; Lyskov, Denis3
1 Institut de Recherche Mathématique Avancée, UMR 7501 Université de Strasbourg et CNRS 7 rue René-Descartes 67000 Strasbourg CEDEX France
2 Department of Mathematical Sciences Chalmers Technical University and the University of Gothenburg SE-412 96 Gothenburg Sweden
3 National Research University Higher School of Economics 20 Myasnitskaya street Moscow 101000 Russia
Algebraic Combinatorics, Volume 7 (2024) no. 3, pp. 801-842.

We introduce a new operad-like structure that we call a reconnectad; the “input” of an element of a reconnectad is a finite simple graph, rather than a finite set, and “compositions” of elements are performed according to the notion of the reconnected complement of a subgraph. The prototypical example of a reconnectad is given by the collection of toric varieties of graph associahedra of Carr and Devadoss, with the structure operations given by inclusions of orbits closures. We develop the general theory of reconnectads, and use it to study the “wonderful reconnectad” assembled from homology groups of complex toric varieties of graph associahedra.

Received:
Revised:
Accepted:
Published online:
DOI: 10.5802/alco.347
Classification: 14M25, 18M70, 18M75
Keywords: Feynman categories, graph associahedra, Koszul duality, toric varieties

Dotsenko, Vladimir 1; Keilthy, Adam 2; Lyskov, Denis 3

1 Institut de Recherche Mathématique Avancée, UMR 7501 Université de Strasbourg et CNRS 7 rue René-Descartes 67000 Strasbourg CEDEX France
2 Department of Mathematical Sciences Chalmers Technical University and the University of Gothenburg SE-412 96 Gothenburg Sweden
3 National Research University Higher School of Economics 20 Myasnitskaya street Moscow 101000 Russia
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights 
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Dotsenko, Vladimir; Keilthy, Adam; Lyskov, Denis. Reconnectads. Algebraic Combinatorics, Volume 7 (2024) no. 3, pp. 801-842. doi : 10.5802/alco.347. https://alco.centre-mersenne.org/articles/10.5802/alco.347/

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