A cell decomposition of the Fulton MacPherson operad
Paolo Salvatore
TL;DR
This paper introduces a cellular decomposition of the Fulton MacPherson operad $FM_2$, compatible with operad composition, using trees with colored edges and labeled vertices, and computes algebraic generating functions for the cells.
Contribution
It provides a new regular cellular decomposition of $FM_2$ compatible with operad structure, indexed by colored trees with labeled vertices, and derives algebraic generating functions.
Findings
Constructed a cellular decomposition compatible with operad composition.
Indexed cells by trees with colored edges and labeled vertices.
Derived algebraic generating functions counting the cells.
Abstract
We construct a small regular cellular decomposition of the Fulton MacPherson operad that is compatible with the operad composition. The cells are indexed by trees with edges of two colors and vertices labelled by cells of the cacti operad. We compute the generating functions counting the cells, that are algebraic.
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Taxonomy
TopicsAdvanced Topics in Algebra · Algebraic structures and combinatorial models · Rings, Modules, and Algebras