Hi everyone, First my background, I'm a junior in physics and math. I've taken griffiths QM, EM (first semester only so far), mechanics and such. In terms of math, I've taken an applied algebra and linear algebra course. I've learned some GR from Sean Carroll's text and a short course in GR by nightingdale. So, I'm looking for a book that covers topics in geometry, topology and physics and how they interrelate. I have some basic knowledge of topology from Munkres and I've learned some Riemannian/semi Riemannian from Tensor Geometry by Dodson and Poston. I've found plenty of books but I'm not sure where to start/what books are good for my level. Any recommendations?
I've heard nothing but good things from "Topology and Geometry for Physicists" by Nash and Sen. However, if you wanted the pure exposure, then of course I doubt you'll find any better than Munkres.
There is another excellent book on precisely this topic. It is Nakahara's "Geometry, Topology, and Physics". Every chapter pretty much covers a course that you'd need to take an entire semester of mathematics to understand. It is extremely terse at times, but I've found it primarily useful to get a nice overview of a topic quickly and then use other resources to zoom in on and learn the details of whatever seems relevant to what I'm interested in. It is a very fun book to read, too - I kept it by my bed for the first several months after I bought it since I liked to read it before going to sleep.
A Course in Modern Mathematical Physics: Groups, Hilbert Space and Differential Geometry by Peter Szekeres http://www.amazon.com/Course-Modern...=sr_1_1?s=books&ie=UTF8&qid=1310821634&sr=1-1 Topology, Geometry and Gauge fields: Foundations by Gregory L. Naber http://www.amazon.com/Topology-Geometry-Gauge-fields-Foundations/dp/0387949461 Topology, Geometry and Gauge fields: Intertions by Gregory L. Naber http://www.amazon.com/gp/product/14..._m=ATVPDKIKX0DER&pf_rd_r=1A81XKFNYEYB76400JND
Divisionbyzero: that book looks interesting, its written by physicists so it definitely seems like something I'd like to read. I'm not a big fan of the pure exposure thing. Monocles: I've seen that book and I knew someone would bring it up. It seems like a good book if a little dense. I may tackle that one later George jones: The course in mathematical physics looks interesting. From the preface it appears oriented towards someone with my background. The other two appear a little too complex. I'll have to see. Thanks for the advice! looking forward to getting started.