Knot Theory

Bachelor's Thesis about Knots and the Jones Polynomial

The following PDF, titled Nusos i el polinomi de Jones, is part of my Final Degree Thesis which was done under the supervision of Joan Porti Piqué. In it, I present an introductory study on knot theory, focusing on algebraic invariants, with a special emphasis on the Jones polynomial. I explore how knots can be classified, particularly for lower-order knots, and discuss some applications of knot theory in fields like quantum computing and molecular biology.

My study begins with a historical overview of knots in human culture and mathematics, explaining their topological properties and key developments in the field. I then introduce fundamental definitions and classifications of knots, highlighting essential concepts such as Reidemeister moves, knot invariants, and the Jones polynomial. In the final sections, I delve into applications, demonstrating the real-world significance of knot theory.

How to Download the Project from GitHub

The document can be found in the following GitHub repository:
🔗 https://github.com/Tutusaus/Knot_Theory

To download the full project, follow these steps:

1. Download as a ZIP File

  • Open the repository link in your browser.
  • Click on the green “Code” button.
  • Select “Download ZIP”.
  • Extract the ZIP file on your computer.

If you have Git installed, open a terminal and run:

git clone https://github.com/Tutusaus/Knot_Theory.git

This will create a local copy of the repository on your computer.

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