Reconnectads
Category Theory
2024-11-28 v2 Combinatorics
K-Theory and Homology
Abstract
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.
Cite
@article{arxiv.2211.15754,
title = {Reconnectads},
author = {Vladimir Dotsenko and Adam Keilthy and Denis Lyskov},
journal= {arXiv preprint arXiv:2211.15754},
year = {2024}
}
Comments
44 pages, submitted version