String topology coproduct and Turaev cobracket on surfaces
Fuente:
arXiv
Guardado en:
| Autores principales: | , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2025
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866912633350782976 |
|---|---|
| author | Hartenstein, Jana Stegemeyer, Maximilian |
| author_facet | Hartenstein, Jana Stegemeyer, Maximilian |
| contents | The string topology coproduct on the homology of the free loop space of a closed manifold induces a string cobracket on $S^1$-equivariant homology. We give a complete computation of the string topology coproduct for surfaces of higher genus by describing an algorithm which computes the coproduct of a cyclic word in terms of generators of the fundamental group of the surface. We further show that the string cobracket is the negative of the Turaev cobracket. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_05997 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | String topology coproduct and Turaev cobracket on surfaces Hartenstein, Jana Stegemeyer, Maximilian Algebraic Topology Geometric Topology 55P50, 57K20 The string topology coproduct on the homology of the free loop space of a closed manifold induces a string cobracket on $S^1$-equivariant homology. We give a complete computation of the string topology coproduct for surfaces of higher genus by describing an algorithm which computes the coproduct of a cyclic word in terms of generators of the fundamental group of the surface. We further show that the string cobracket is the negative of the Turaev cobracket. |
| title | String topology coproduct and Turaev cobracket on surfaces |
| topic | Algebraic Topology Geometric Topology 55P50, 57K20 |
| url | https://arxiv.org/abs/2510.05997 |