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...
Saved in:
Main Author: | |
---|---|
Other Authors: | |
Format: | Final Year Project |
Language: | English |
Published: |
Nanyang Technological University
2020
|
Subjects: | |
Online Access: | https://hdl.handle.net/10356/138522 |
Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
Institution: | Nanyang Technological University |
Language: | English |
Summary: | 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. |
---|