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

Vladimir Dotsenko; Eduardo Hoefel; Sergey Shadrin; Grigory Solomadin

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arXiv · 2509.20331

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

Vladimir Dotsenko·Eduardo Hoefel·Sergey Shadrin·Grigory Solomadin

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Abstract

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.

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BibTeX RIS

Vladimir Dotsenko, Eduardo Hoefel, Sergey Shadrin, Grigory Solomadin. 2025-09-24. Operads of moduli spaces of points in $\mathbb{C}^d$ revisited. https://arxiv.org/abs/2509.20331

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