Dissertation
Properties of the Goldman Lie algebra
University of Iowa
Doctor of Philosophy (PhD), University of Iowa
Spring 2021
DOI: 10.17077/etd.005818
Abstract
The Goldman Lie algebra is a Lie algebra of free homotopy classes of curves on surfaces with a bracket given by summing over all possible concatenations. This Lie algebra shares a wealth of connections to skein theory, the character variety, and moduli spaces of geometric structures on surfaces. This thesis is concerned with the study of its properties as a pathway to gleaning more information about the structures it relates to.
Details
- Title: Subtitle
- Properties of the Goldman Lie algebra
- Creators
- Mohamed Imad Bakhira
- Contributors
- Benjamin Cooper (Advisor)Charles Frohman (Committee Member)Mohammad Farajzadeh Tehrani (Committee Member)Miodrag Iovanov (Committee Member)Ryan Kinser (Committee Member)
- Resource Type
- Dissertation
- Degree Awarded
- Doctor of Philosophy (PhD), University of Iowa
- Degree in
- Mathematics
- Date degree season
- Spring 2021
- DOI
- 10.17077/etd.005818
- Publisher
- University of Iowa
- Number of pages
- viii, 74 pages
- Copyright
- Copyright 2021 Mohamed Imad Bakhira
- Language
- English
- Description illustrations
- illustrations
- Description bibliographic
- Includes bibliographical references (pages 73-74)
- Public Abstract (ETD)
The Goldman Lie Algebra is a Lie algebra which describes the behavior of curves and their intersections and resolutions on surfaces. It carries information about geometric structures with which the surface may be endowed and appears as a classical mechanistic counterpart to the quantum nature of knots in 3-dimensional space. In this thesis, we discover new properties of the Goldman Lie Algebra and its related knot structure and consequently construct a new variant of the Goldman Lie Algebra.
- Academic Unit
- Mathematics
- Record Identifier
- 9984097276602771
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