There is a saying "Do you read the masters?"

I want to read some basic papers in Topology/geometry...

I can not clearly state what is basic as of now...

My back ground includes course in

  • Category theory, Some group Cohomology
  • Algebraic topology
  • Differential forms, deRham cohomology
  • Representation theory of finite groups
  • Lie groups and Lie algebras

I am interested to learn some $K$ theory.

The reason I am interested is I did a course in representation theory(from Serre's Book).. In that there is a discussion about Grothendick group ... We denote it by $K(\mathcal{F})$.. Though i do not understand it it was fascinating... Then I saw that this $K$ is the $K$ in $K$- theory...

I was reading some smooth manifolds and came across with what is called tangent bundle, vector bundle, fibre bundle.. Then realized this fibre bundle has some thing to do with fibrations and vector bundles are related to $K$- theory...

So, all that i want to ask is a suggestion about the papers that i can read with this background.

PS : I believe this can be made to community wiki at least. This is a question that asks to refer some books and i have given details.


closed as primarily opinion-based by YCor, Alex Degtyarev, Fernando Muro, András Bátkai, Daniel Moskovich Feb 7 '16 at 21:32

Many good questions generate some degree of opinion based on expert experience, but answers to this question will tend to be almost entirely based on opinions, rather than facts, references, or specific expertise. If this question can be reworded to fit the rules in the help center, please edit the question.

  • $\begingroup$ Three papers which are often considered as classics: maths.ed.ac.uk/~aar/papers/thomcob.pdf (Thom: Quelques proprietes globales des varietes differentiables) and link.springer.com/article/10.1007%2FBF02564562 (Serre: Cohomologie modulo 2 des complexes d'Eilenberg-MacLane) and jstor.org/stable/1969789 (Serre: Groupes d'homotopie et classes des groupes abeliens) $\endgroup$ – ThiKu Feb 8 '16 at 12:24
  • $\begingroup$ @ThiKu : Thanks for your suggestion.. I can read only english. Please see if you suggest some thing in that lines and i have told you my background.. $\endgroup$ – user86358 Feb 8 '16 at 17:34

It is worth noting that in $K$-theory one can read `the masters' without that necessarily meaning reading research papers. Specifically, if you are interested in topological $K$-theory, then Atiyah's book is still a very good introduction. Similarly, Milnor's book is an excellent introduction to the lower algebraic $K$-groups.

  • $\begingroup$ I can not upvote as i do not have sufficient reputation... Yesterday, i have checked that book by atiyah... I could not see it properly due to time constraint.. I will definitely see that today.. I have checked table of contents in Milnor's book and i think i do not have enough background to read that.. But atiyah, Yes i will definitely try to read.. $\endgroup$ – user86358 Feb 7 '16 at 20:56