Exploring Topology and Representation Theory: Recommended Books and Resources

[linkedlister]

Hello,

I have a general interest in teaching myself topology to build up to moving onto Representation theory. I have chosen M.A. Armstrongs's book "Basic Topology" as my start.

My Question... where would you all recommend I go from there. I took top in undergrad and that was the book we used. What are some other highly recommended books on the subject. And what other books do you suggest to get me up to speed and over to my goal of reading through a book on Lie algebras -- or did I miss my mark and should have gone for geometry?

 

[linkedlister]

I see i may have posted this in the wrong forum .. I will repost in learning materials..

 

[linkedlister]

Unfortunately i do not have permission to post a question in the Learning materials forum group... so if anyone could post answers to the question here - it would be most appreciated.

 

[Tinyboss]

Topology by Munkres is fantastic.

 

[micromass]

Why have you chosen for armstrong's book?? The book is horrible, I wouldn't recommend it to anybody. Sure, if you know a bit of topology already, then armstrong's book could be good. But don't try to use it to teach yourself.

Go for Munkres instead, it's a wonderful book especially suited for self-study!

 

[Fredrik]

There's a science book forum. You can use the report button to request that the thread be moved there. And yeah, Munkres.

 

[Landau]

Munkres or Armstrong? Nah... (I don't like Armstrong's writing style, just like his Groups & Symmetries. Munkres' book has a slow pace, but is extensive.)
Willard or Jänich...yeah!

 

[lavinia]

Hello,

I have a general interest in teaching myself topology to build up to moving onto Representation theory. I have chosen M.A. Armstrongs's book "Basic Topology" as my start.

My Question... where would you all recommend I go from there. I took top in undergrad and that was the book we used. What are some other highly recommended books on the subject. And what other books do you suggest to get me up to speed and over to my goal of reading through a book on Lie algebras -- or did I miss my mark and should have gone for geometry?

I believe that topological ideas arise naturally in the study of complex analysis. That's what I would do not knowing anything about your long term goals.

 

[quasar987]

I don't recommand Munkres for self study as it contains too much stuff you'll never need use or see again in your life. If you had someone tell you exactly what part of general topology are relevant for your long term goalds, ok, but otherwise, how would you know that you're wasting time reading about T¼ spaces?

If your goal is to understand Lie groups and their Lie algebra, then what you need is the general theory of smooth manifolds. IMO, the shortest and easiest way to do this is to read John Lee's Introduction to Smooth Manifolds where Lie algebras of Lie groups are introduced as early as page 93. Since you've taken topology as an undergrad, you can read the appendix on topology to refresh your memory, or pick up Lee's Introduction to Topological Manifolds, which tells you what you need to know and skip the rest.

 

[Landau]

If you quickly want to learn about Lie algebra's, you don't even need to know about smooth manifolds (the relation between Lie groups can come later). Pick up Hymphrey's "Introduction to Lie Algebras and Representation Theory", the only prerequisite is a decent algebra background. Or even better, take up Erdmann's Introduction to Lie Algebras.

 

[mathwonk]

there is a little section on linear groups in the book Algebra, by Michael Artin which only uses a little topology. See if you can read that.

 

[Fredrik]

Lie groups, Lie algebras, and representations: an elementary introduction, by Brian Hall completely avoids differential geometry by focusing on Lie groups whose members are matrices. This includes almost all groups that are relevant in physics.

I completely agree with what quasar987 said about Munkres and Lee. (Munkres is great, but it contains a lot of stuff you don't need. Lee's books are excellent).

You don't really need topology for the stuff about Lie groups and Lie algebras. You just need a little to understand the definition of a manifold.