A Primer on Homotopy Colimits
by Daniel Dugger
Publisher: University of Oregon 2008
Number of pages: 72
This is an expository paper on homotopy colimits and homotopy limits. These are constructions which should arguably be in the toolkit of every modern algebraic topologist. Many proofs are avoided, or perhaps just sketched.
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by Carlo Mazza, Vladimir Voevodsky, Charles Weibel - AMS
This book provides an account of the triangulated theory of motives. Its purpose is to introduce Motivic Cohomology, to develop its main properties, and finally to relate it to other known invariants of algebraic varieties and rings.
by J. S. Milne
These are the notes for a course taught at the University of Michigan in 1989 and 1998. The emphasis is on heuristic arguments rather than formal proofs and on varieties rather than schemes. The notes also discuss the proof of the Weil conjectures.
by Bjorn Ian Dundas - NTNU
This is not an introductory textbook in algebraic topology, these notes attempt to give an overview of the parts of algebraic topology, and in particular homotopy theory, which are needed in order to appreciate that side of motivic homotopy theory.
by Boris Dubrovin - arXiv
These lecture notes are devoted to the theory of equations of associativity describing geometry of moduli spaces of 2D topological field theories. Topics: WDVV equations and Frobenius manifolds; Polynomial solutions of WDVV; Symmetries of WDVV; etc.