A surgery approach to abelian quotients of the level 2 congruence group and the Torelli group

Lewis, Tudur (2024) A surgery approach to abelian quotients of the level 2 congruence group and the Torelli group. PhD thesis, University of Glasgow.

Abstract

We provide a unified framework for studying two families of maps: the Birman–Craggs maps of the Torelli group, and Sato’s maps of the level 2 congruence subgroup of the mapping class group. Our framework gives new, elementary proofs that both families of maps are homomorphisms, gives a direct method for evaluating these maps on Dehn twists, and relates the two families when restricted to the Torelli group. Our methods involve 3-manifold techniques that do not depend on results in 4–manifold theory as in the original constructions, giving an answer to a question of Dennis Johnson. We also find a relation between an extension of the Birman–Craggs maps to the level 2 congruence subgroup, and Meyer’s signature cocycle.

• Item Type: Thesis (PhD)
• Qualification Level: Doctoral
• Subjects: Q Science > QA Mathematics
• Colleges/Schools: College of Science and Engineering > School of Mathematics and Statistics > Mathematics
• Supervisor's Name: Brendle, Professor Tara, Gadre, Dr. Vaibhav and Owens, Professor Brenda
• Date of Award: 2024
• Depositing User: Theses Team
• Unique ID: glathesis:2024-84606
• Copyright: Copyright of this thesis is held by the author.
• Date Deposited: 08 Oct 2024 15:46
• Last Modified: 08 Oct 2024 15:48
• Thesis DOI: 10.5525/gla.thesis.84606
• URI: https://theses.gla.ac.uk/id/eprint/84606