I am doing PhD in Leavitt Path Algebras (LPAs). While going through some recent works on LPAs I found this paper titled K-Theory of Leavitt path algebras by Ara etal. I tried reading it, but failed vehemently.
Consequently, I tried self learning Algebraic K-Theory from Bruce Magurn, but the book seemed to be not sufficient to cover the ideas in the aforementioned paper. Accordingly, I tried following Weibel's K-book, Bass's Algebraic K-Theory and Srinivas's Algebraic K-Theory. Now, in almost all these books that I have mentioned, I found that they require a significant understanding of Algebraic Topology and Homological Algebra and I do not have a very strong hold of them.
So, I was wondering what should be my possible course of action to work out the above paper. My current objective is to understand the material in the paper and at the same time learn Algebraic K-Theory without entering much into the realm of Topological K-Theory or Algebraic Topology. I guess I need a text that deals with K-Theory in a purely algebraic setting. Additionally, what is the difference between these two school of thoughts namely Algebraic K-Theory and Topological K-Theory is there any resource that provides the distinction between them in basic terms.
Furthermore, if I want to learn more of K-Theory and pursue a research career in it. What are the prerequisites ? Up to what degree should I learn Algebraic Topology, Algebraic Geometry or any other subject for the matter ?
I am aware that there are a lot of questions on recommendations for K-Theory in this site. Unfortunately, those recommendations didn't help me much.