The trace field of hyperbolic gluings
BORIS DOI
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.
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.
Date of Publication
2019
Year of graduation
2019
Theses Type
dissertation
Subject(s)
Language(s)
en
Author(s)
Mila, Olivier |
Faculty/Graduate School
Institute
Access(Rights)
open.access
Primary OA Publication
true