Properadic coformality of spheres
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866911526111150080 |
|---|---|
| author | Emprin, Coline Takeda, Alex |
| author_facet | Emprin, Coline Takeda, Alex |
| contents | We define a properad $Y^{(n)}_\infty$ that encodes $n$-pre-Calabi--Yau algebras with vanishing copairing. These algebras include chains on the based loop space of any space $X$ endowed with a fundamental class $[X]$ such that $(X,[X])$ satisfies Poincaré duality of degree $n \geqslant 1$ with local system coefficients, such as an oriented manifold. Extending the notion of coformality of spaces, we define coformality of such a pair $(X,[X])$ in terms of properadic formality of $Y^{(n)}_\infty$-algebra structures on $C_*(ΩX)$. Using a refined version of properadic Kaledin classes, we establish the intrinsic coformality of all spheres in characteristic zero. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_04297 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Properadic coformality of spheres Emprin, Coline Takeda, Alex Algebraic Topology Quantum Algebra 18M85 (Primary) 16E40, 55P35, 55S35 (Secondary) We define a properad $Y^{(n)}_\infty$ that encodes $n$-pre-Calabi--Yau algebras with vanishing copairing. These algebras include chains on the based loop space of any space $X$ endowed with a fundamental class $[X]$ such that $(X,[X])$ satisfies Poincaré duality of degree $n \geqslant 1$ with local system coefficients, such as an oriented manifold. Extending the notion of coformality of spaces, we define coformality of such a pair $(X,[X])$ in terms of properadic formality of $Y^{(n)}_\infty$-algebra structures on $C_*(ΩX)$. Using a refined version of properadic Kaledin classes, we establish the intrinsic coformality of all spheres in characteristic zero. |
| title | Properadic coformality of spheres |
| topic | Algebraic Topology Quantum Algebra 18M85 (Primary) 16E40, 55P35, 55S35 (Secondary) |
| url | https://arxiv.org/abs/2503.04297 |