Representation Varieties of Once-Punctured Torus Bundles

Ever since Thurston exhibited the central role played by hyperbolic geometry in the study of three-dimensional manifolds, many links have been established between the topology and geometry of a three-manifold and the set of all representations of its fundamental group into the group of orientation preserving isometries of three-dimensional hyperbolic space.

This project examines these so-called representation varieties for the key class of once-punctured torus bundles. The first aim is to obtain quantitative and qualitative results on the topology and algebraic geometry of these varieties. The second aim is related to the study of profinite completions of the fundamental groups, and examines finite quotients arising from irreducible representations.

Youheng Yao

The University of Sydney

Youheng Yao is a second-year undergraduate majoring in mathematics and data science at The University of Sydney. He is interested in various fields in pure math, particularly algebra and geometry. He hopes to do the Honours and postgraduate studies in the field in the future.

You may be interested in

Juan Avila Molina

Juan Avila Molina

Finding the Body of Minimal Resistance
Ngoc Phuong Van Nguyen

Ngoc Phuong Van Nguyen

Mathematical Modelling of Harmful Algal Blooms
Nelly Tucker

Nelly Tucker

Long memory random walks
Elizabeth Rose

Elizabeth Rose

Incorporating Spatio-Temporal Convection Effects in Classical Snowball Earth Models
Contact Us

We're not around right now. But you can send us an email and we'll get back to you, asap.

Not readable? Change text.