Braid Groups at undergraduate level

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SUMMARY

The discussion centers on the study of Braid Groups, particularly at the undergraduate level. M.A. Armstrong's book "Groups and Symmetry" introduces Braid Groups, but participants seek accessible resources for beginners. Peter emphasizes the necessity of a foundational understanding of topology for serious study, suggesting that while one can explore Braid Groups with only abstract algebra knowledge, a deeper comprehension requires topology. For initial exploration, Baez's website is recommended as a valuable resource.

PREREQUISITES
  • Understanding of abstract algebra
  • Basic knowledge of topology
  • Familiarity with group theory concepts
  • Exposure to mathematical literature, particularly in algebraic topology
NEXT STEPS
  • Explore M.A. Armstrong's "Groups and Symmetry" for foundational concepts
  • Visit Baez's website on Braid Groups for introductory insights
  • Study topology fundamentals to enhance understanding of Braid Groups
  • Research advanced texts on Braid Groups, such as those by Kassel
USEFUL FOR

Undergraduate mathematics students, educators in abstract algebra and topology, and anyone interested in the foundational aspects of Braid Groups.

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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
 
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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:

https://www.physicsforums.com/newreply.php?do=newreply&noquote=1&p=3819446

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
 

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