Operads of moduli spaces of points in $\mathbb{C}^d$ revisited

Fuente: arXiv
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Autores principales: Dotsenko, Vladimir, Hoefel, Eduardo, Shadrin, Sergey, Solomadin, Grigory
Formato: Preprint
Publicado: 2025
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author Dotsenko, Vladimir
Hoefel, Eduardo
Shadrin, Sergey
Solomadin, Grigory
author_facet Dotsenko, Vladimir
Hoefel, Eduardo
Shadrin, Sergey
Solomadin, Grigory
contents We study the operad structure on the homology of moduli spaces of pointed rooted trees of $d$-dimensional projective spaces, introduced by Chen, Gibney and Krashen a couple of decades ago. We describe this operad by generators and relations, show that it is homotopy Koszul, exhibit a Givental-type action on representations of that operad, and prove that this operad represents the homotopy quotient of the operad of chains of $S^1$-framed little $2d$-disks by its natural circle action. Our approach also sheds new light on the $d=1$ case, revealing a new combinatorial way to write the original Givental formulas.
format Preprint
id arxiv_https___arxiv_org_abs_2509_20331
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Operads of moduli spaces of points in $\mathbb{C}^d$ revisited
Dotsenko, Vladimir
Hoefel, Eduardo
Shadrin, Sergey
Solomadin, Grigory
Algebraic Topology
Mathematical Physics
Algebraic Geometry
K-Theory and Homology
Quantum Algebra
We study the operad structure on the homology of moduli spaces of pointed rooted trees of $d$-dimensional projective spaces, introduced by Chen, Gibney and Krashen a couple of decades ago. We describe this operad by generators and relations, show that it is homotopy Koszul, exhibit a Givental-type action on representations of that operad, and prove that this operad represents the homotopy quotient of the operad of chains of $S^1$-framed little $2d$-disks by its natural circle action. Our approach also sheds new light on the $d=1$ case, revealing a new combinatorial way to write the original Givental formulas.
title Operads of moduli spaces of points in $\mathbb{C}^d$ revisited
topic Algebraic Topology
Mathematical Physics
Algebraic Geometry
K-Theory and Homology
Quantum Algebra
url https://arxiv.org/abs/2509.20331