The handlebody group and the images of the second Johnson homomorphism
| Autor: | Faes, Quentin |
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| Rok vydání: | 2020 |
| Předmět: | |
| Zdroj: | Algebr. Geom. Topol. 23 (2023) 243-293 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.2140/agt.2023.23.243 |
| Popis: | Given an oriented surface bounding a handlebody, we study the subgroup of its mapping class group defined as the intersection of the handlebody group and the second term of the Johnson filtration: $\mathcal{A} \cap J_2$. We introduce two trace-like operators, inspired by Morita's trace, and show that their kernels coincide with the images by the second Johnson homomorphism $\tau_2$ of $J_2$ and $\mathcal{A} \cap J_2$, respectively. In particular, we answer by the negative to a question asked by Levine about an algebraic description of $\tau_2(\mathcal{A} \cap J_2)$. By the same techniques, and for a Heegaard surface in $S^3$, we also compute the image by $\tau_2$ of the intersection of the Goeritz group $\mathcal{G}$ with $J_2$. Comment: 33 pages, 5 figures. In the second version, one appendix has been added. Also, some minor changes have been done, including descriptions of the space of homology 3-spheres using the second and third term of the Johnson filtration. In the final version, we included more precise definitions, and some new references |
| Databáze: | arXiv |
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