The Getzler-Gauss-Manin connection and Kontsevich-Soibelman operations on the periodic cyclic homology
Fuente:
arXiv
Guardado en:
| Autor principal: | |
|---|---|
| Formato: | Preprint |
| Publicado: |
2026
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866911393485160448 |
|---|---|
| author | Chen, Zihong |
| author_facet | Chen, Zihong |
| contents | We study equivariant operations on the periodic cyclic homology of a dg algebra that arise from the chain level action of the two-colored Kontsevich-Soibelman operad. Using classical computations of Cohen [Coh], we explicitly compute a set of generators for these operations under composition, and show that they agree with the p-fold equivariant cap products previously studied by the author [Che2] in relation to equivariant Gromov-Witten theory with mod p coefficients. The main technical novelty is a re-formulation of the Kontsevich-Soibelman operad in terms of a two-colored version of the cacti operad, and a proof that it is equivariantly quasi-equivalent to the two-colored operad of little disks on a disk/cylinder. We give applications of the main results to symplectic topology, and more specifically, arithmetic aspects of Fukaya category and classical obstructions to realizing a middle cohomology class of a symplectic manifold by Lagrangian submanifold |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_16437 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The Getzler-Gauss-Manin connection and Kontsevich-Soibelman operations on the periodic cyclic homology Chen, Zihong Quantum Algebra Algebraic Topology Symplectic Geometry We study equivariant operations on the periodic cyclic homology of a dg algebra that arise from the chain level action of the two-colored Kontsevich-Soibelman operad. Using classical computations of Cohen [Coh], we explicitly compute a set of generators for these operations under composition, and show that they agree with the p-fold equivariant cap products previously studied by the author [Che2] in relation to equivariant Gromov-Witten theory with mod p coefficients. The main technical novelty is a re-formulation of the Kontsevich-Soibelman operad in terms of a two-colored version of the cacti operad, and a proof that it is equivariantly quasi-equivalent to the two-colored operad of little disks on a disk/cylinder. We give applications of the main results to symplectic topology, and more specifically, arithmetic aspects of Fukaya category and classical obstructions to realizing a middle cohomology class of a symplectic manifold by Lagrangian submanifold |
| title | The Getzler-Gauss-Manin connection and Kontsevich-Soibelman operations on the periodic cyclic homology |
| topic | Quantum Algebra Algebraic Topology Symplectic Geometry |
| url | https://arxiv.org/abs/2601.16437 |