# Braid Groups at undergraduate level

• Math Amateur
The book "Braid Groups: A Survey" by Kassel and Turaev is a good resource for studying Braid GroupsIn summary, M.A. Armstrong's book "Groups and Symmetry" introduces the topic of Braid Groups. There is an undergraduate level book by Kassel and Turaev, "Braid Groups: A Survey," and a website by Baez that can be used to study Braid Groups without a background in topology. However, a good understanding of topology is recommended for a serious study of Braid Groups.
Math Amateur
Gold Member
MHB
In M.A. Armstrongs book "Groups and Symmetry" in Chapter 12 he introduces the reader to the fascinating topic of Braid Groups.

Does anyone know of a book at undergraduate level (or even a popular book) that deals with Braid Groups

Can you progress with Braid Groups if you lack a sophisticated knowledge of topology? That is, how far can you progress with a study of Braid Groups if you only have a good knowledge of abstract algebra?

Peter

Well, I only know about the topology side of it. My adviser and Kassel wrote a book about braids, but it's more like beginning graduate-level:

I wouldn't recommend seriously studying braids without first doing some topology.

However, if you just want to dip your toes in the subject, without needing to know topology, I highly recommend Baez's website:

http://math.ucr.edu/home/baez/braids.html

Last edited by a moderator:
Thanks

Recommended website looks really interesting

Peter

## 1. What are braid groups and why are they important in mathematics?

Braid groups are mathematical groups that represent the movement of strands or strings without allowing them to twist or cross over each other. They are important in mathematics because they have applications in various fields such as topology, knot theory, and cryptography.

## 2. How are braid groups different from other types of mathematical groups?

Braid groups are non-commutative, meaning that the order in which operations are performed matters. This is unlike other groups such as permutation groups, which are commutative. Additionally, braid groups have infinite order, meaning that there are an infinite number of possible braid configurations.

## 3. What are some real-world applications of braid groups?

Braid groups have applications in various fields such as physics, chemistry, and biology. In physics, braid groups are used to describe the behavior of particles in certain physical systems. In chemistry, they are used to study molecular structures. In biology, braid groups are used to analyze DNA sequences.

## 4. How are braid groups related to knot theory?

Braid groups are closely related to knot theory, as they can be used to represent and study different types of knots. In fact, every knot can be represented as a braid, and the properties of braid groups can be used to classify and distinguish between different types of knots.

## 5. Can braid groups be studied at the undergraduate level?

Yes, braid groups can be studied at the undergraduate level, although a solid foundation in abstract algebra and group theory is necessary. Many undergraduate courses in mathematics cover braid groups as part of their curriculum, and there are also numerous resources available online for self-study.

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