I am looking for as gentle of possible of an introduction to Kontsevich-Soibelman's theory of motivic DT-invariants. Specifically I am interested in the algebraic aspects of the theory and the relation with cluster categories. Obviously there is Kontsevich and Soibelman's 150 page paper on the subject, but words like etale and stack tend to make me panic. I am much more comfortable with 3-Calabi-Yau categories than 3 dimensional Calabi-Yau varieties.

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gentlenessI'd be interested in) For non-refined DT invariants I find Bridgeland's Introduction to Motivic Hall Algebras great. In the end etale just meanslocal diffeomorphism(or relative Kahler differentials zero if that's clearer to you o_O) and stacks are just a fact of life and one ends up thinking about them just as any other space (I guess). At least theideaof a motivic Hall algebra is quite simple. – Yosemite Sam Jun 25 '12 at 3:02definitionof motivic DT-invariants. You need moduli stacks of stable objects, the Grothendieck group of (classes of) motives, the construction of the motivic Milnor fibre. Having said that, I think there are two silver linings: 1. None of these concepts are quite as scary as they are sometimes made out to be. (For example, the Grothendieck group of classes of motives is a simpler concept than any category of motives.) 2. Thewall-crossing behaviourof DT-invariants is the interesting and purely algebraic part of the story. See e.g. Keller's notes. – Arend Bayer Jun 25 '12 at 11:42