Mila, Olivier (2019). The trace field of hyperbolic gluings. (Thesis). Universität Bern, Bern

Preview

Text 19mila_o.pdf - Thesis Available under License Creative Commons: Attribution-Noncommercial-No Derivative Works (CC-BY-NC-ND 4.0). Download (941kB) | Preview

Abstract

The first part of the thesis focuses on the study of the adjoint trace field of hyperbolic manifolds, an algebraic invariant introduced by Vinberg and generalizing the invariant trace field of dimension 3. We compute the adjoint trace field in the case of general hyperbolic gluings, and show how it can be used to prove that certain gluings are nonarithmetic. In the second part we introduce and motivate the concept of pseudo-arithmeticity, a notion that encompasses all known examples of hyperbolic manifolds. We then prove that gluings of arithmetic pieces are always pseudo-arithmetic, using results from the first part.

Item Type:	Thesis
Dissertation Type:	Single
Date of Defense:	23 August 2019
Subjects:	500 Science > 510 Mathematics
Institute / Center:	08 Faculty of Science > Department of Mathematics and Statistics > Institute of Mathematics
Depositing User:	Hammer Igor
Date Deposited:	04 Sep 2020 09:08
Last Modified:	07 Sep 2020 10:16
URI:	https://boristheses.unibe.ch/id/eprint/2184

Actions (login required)

View Item