I am a physics undergrad and want to pursue a PhD in maths (geometry or topology). I study it almost completely by myself, as the program in my country offers very less flexibility to take non departmental courses, thought I will be able to take them is a couple of semesters. Anyway, So I was thinking about taking a mini-project of sorts which I can self-study or maybe ask a prof. I had heard about this theorem while studying topological solitons in physics.
What are the prerequisites for studying the Atiyah–Singer theorem. I had a look online, but I couldn't figure out exactly, in what field this is, or what are the prerequisites. Wikipedia says it is a theorem in differential geometry, but obviously what differential geometry I know is insufficient. I know about manifolds, differential forms, lie derivatives, lie groups, and some killing vectors stuff. A look at the material online also talks about some operators in DG which I have never come across. Are there an algebraic topology prerequisites?
Please could you recommend me some references which can take me there?
Thanks in advance!