I'm a PhD student trying to learn the math required to understand Gauge theory. From some reading over the past few weeks, I think I need to learn the following:
- Lie algebra / Lie groups
- Algebraic and geometric Topology
- Differential geometry
I only need understand the material enough to be literate (my research hopes only to use some results from these fields and not to contribute to them). Does anyone have any good recommendations for textbooks that assume little mathematical knowledge beyond some undergrad. courses in linear algebra, vector calc., probability, and PDEs?
In particular, I'm hoping to find a textbook that assumes little prior knowledge while being somewhat brief its exposition (in my reading so far I'm finding myself getting lost in the volume of definitions).
Thanks for reading, I appreciate any suggestions!
edit: hardmath asked where I feel I've been getting lost in definitions. I've started reading "A Course in Modern Mathematical Physics" by Peter Szekeres (suggested by a friend). This seems like a great book and I've learnt a lot in the first few chapters but I'm struggling with the amount of terminology. For example, by chapter 3 my notes contained about 70 definitions.