Skein modules, skein algebra and quantisation

Skein modules are topological invariant for 3-manifolds constructed using knots and links. They are found to have important connections to important physical and mathematical problems. The main connection explored here is the quantisation of character variety, which has application in Physics as...

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Main Author: Lee, Benedict Jia Jie
Other Authors: Andrew James Kricker
Format: Final Year Project
Language:English
Published: Nanyang Technological University 2020
Subjects:
Online Access:https://hdl.handle.net/10356/138522
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Institution: Nanyang Technological University
Language: English
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spelling sg-ntu-dr.10356-1385222023-02-28T23:16:01Z Skein modules, skein algebra and quantisation Lee, Benedict Jia Jie Andrew James Kricker School of Physical and Mathematical Sciences Monash University Daniel Mathews AJKricker@ntu.edu.sg; daniel.mathews@monash.edu Science::Mathematics::Geometry Science::Mathematics::Topology Skein modules are topological invariant for 3-manifolds constructed using knots and links. They are found to have important connections to important physical and mathematical problems. The main connection explored here is the quantisation of character variety, which has application in Physics as well as hyperbolic geometry. In this report, we will look at the work by Le, who developed a cutting map which allows one to describe certain classes of skein algebra as well as construct an important map called the quantum trace map. We will also look at two examples of skein module, two bridge knot complements and mapping torus, where we can describe the skeins using only part of the manifold. Bachelor of Science in Physics 2020-05-07T12:46:56Z 2020-05-07T12:46:56Z 2020 Final Year Project (FYP) https://hdl.handle.net/10356/138522 en application/pdf Nanyang Technological University
institution Nanyang Technological University
building NTU Library
continent Asia
country Singapore
Singapore
content_provider NTU Library
collection DR-NTU
language English
topic Science::Mathematics::Geometry
Science::Mathematics::Topology
spellingShingle Science::Mathematics::Geometry
Science::Mathematics::Topology
Lee, Benedict Jia Jie
Skein modules, skein algebra and quantisation
description Skein modules are topological invariant for 3-manifolds constructed using knots and links. They are found to have important connections to important physical and mathematical problems. The main connection explored here is the quantisation of character variety, which has application in Physics as well as hyperbolic geometry. In this report, we will look at the work by Le, who developed a cutting map which allows one to describe certain classes of skein algebra as well as construct an important map called the quantum trace map. We will also look at two examples of skein module, two bridge knot complements and mapping torus, where we can describe the skeins using only part of the manifold.
author2 Andrew James Kricker
author_facet Andrew James Kricker
Lee, Benedict Jia Jie
format Final Year Project
author Lee, Benedict Jia Jie
author_sort Lee, Benedict Jia Jie
title Skein modules, skein algebra and quantisation
title_short Skein modules, skein algebra and quantisation
title_full Skein modules, skein algebra and quantisation
title_fullStr Skein modules, skein algebra and quantisation
title_full_unstemmed Skein modules, skein algebra and quantisation
title_sort skein modules, skein algebra and quantisation
publisher Nanyang Technological University
publishDate 2020
url https://hdl.handle.net/10356/138522
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