Operads of moduli spaces of points in $\mathbb{C}^d$ revisited
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arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Acceso en línea: | |
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| _version_ | 1866911173898665984 |
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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 |