The handlebody group and the images of the second Johnson homomorphism - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Algebraic and Geometric Topology Année : 2023

The handlebody group and the images of the second Johnson homomorphism

Quentin Faes
  • Fonction : Auteur
  • PersonId : 1124741

Résumé

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; A n J2. 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 r2 of J2 and A n J2, respectively. In particular, we answer in the negative a question asked by Levine about an algebraic description of r2(A n J2). By the same techniques, and for a Heegaard surface in S3, we also compute the image by r2 of the intersection of the Goeritz group g with J2.

Dates et versions

hal-04362169 , version 1 (22-12-2023)

Identifiants

Citer

Quentin Faes. The handlebody group and the images of the second Johnson homomorphism. Algebraic and Geometric Topology, 2023, 23 (1), pp.243-293. ⟨10.2140/agt.2023.23.243⟩. ⟨hal-04362169⟩
4 Consultations
0 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More