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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2020
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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 |
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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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1759856293702533120 |