# Exploring 4D Knot Theory: Reidermeister Moves & Movie Representation

• mersecske
In summary, the conversation discusses the need for freely available resources on 4D knots theory, specifically the 4D generalization of Reidermeister moves and the movie representation. The conversation suggests searching for abstracts on the internet and utilizing a local university library for photocopying. It also mentions the possibility of finding movies on websites such as Youtube. The conversation ends with a request for specific paper titles that introduce 4D knot theory and Reidermeister moves.
mersecske
I need a free description with illustrations on 4D knots theory,
especially the 4D generalization of Reidermeister moves and
the movie represantation.

Where can I find a freely available paper?

mersecske said:
Where can I find a freely available paper?

Search for abstracts on the internet then photocopy the content from your local university library?

mersecske said:

Which part is not usable? Are you unable to find references/abstracts on the internet? Or do you not have access to a suitable university library?

I suspect you'll need a website to find movies, and there are surely free ones. Tried Youtube?

Please tell me some title of papers which introduce 4D knot theory and Reidermeister moves are intruduced as well.

## 1. What is 4D knot theory?

4D knot theory is a branch of mathematics that studies the properties and behavior of knots in four-dimensional space. It involves the use of abstract algebra, topology, and geometry to understand the structure of knots in higher dimensions.

## 2. What are Reidermeister moves?

Reidermeister moves are a set of three elementary moves that can be performed on knots in four-dimensional space. These moves involve crossing or uncrossing strands of a knot in a specific way and are used to prove the equivalence of different knot diagrams.

## 3. How are Reidermeister moves related to 4D knot theory?

Reidermeister moves are an important tool in 4D knot theory, as they allow mathematicians to manipulate and analyze knots in four-dimensional space. By using Reidermeister moves, mathematicians can prove the equivalence of different knot diagrams, which is crucial in understanding the structure of knots in higher dimensions.

## 4. What is the movie representation of knots?

The movie representation of knots is a method for representing and studying knots in four-dimensional space. It involves breaking down a knot into a series of two-dimensional diagrams, called "movies," and using Reidermeister moves to analyze and understand the knot's structure in four dimensions.

## 5. Why is exploring 4D knot theory important?

Exploring 4D knot theory is important because it helps us understand the structure of knots in higher dimensions, which has implications in fields such as physics, biology, and chemistry. It also allows us to develop new mathematical techniques and tools for studying knots and other complex structures in higher dimensions.

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