Hyperbolic Structures On Weave Complements

Author

Indra Shottland

Date of Award

2010

Document Type

Thesis

Degree Name

Bachelors

Department

Natural Sciences

First Advisor

McDonald, Patrick

Keywords

Hyperbolic, 3-Manifold, Weave Complement, Alternating Weave, Augmented Weave

Area of Concentration

Mathematics

Abstract

We study a class of hyperbolic 3-manifold with non-finitely generated fundamental group: weave complements. We describe how to endow these spaces with a hyperbolic structure by (1) decomposing them into ideal octahedra and (2) realizing these ideal octahedra in hyperbolic space. Conditions are given which ensure that an alternating weave is hyperbolic. We then extend our results to augmented alternating weaves.

Recommended Citation

Shottland, Indra, "Hyperbolic Structures On Weave Complements" (2010). Theses & ETDs. 4332.
https://digitalcommons.ncf.edu/theses_etds/4332