Algebraic and Geometric Topology
by Andrew Ranicki, Norman Levitt, Frank Quinn
Publisher: Springer 1985
Number of pages: 436
The articles in this volume present original research on a wide range of topics in modern topology. They include important new material on the algebraic K-theory of spaces, the algebraic obstructions to surgery and finiteness, geometric and chain complexes, characteristic classes, and transformation groups.
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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 Danny Calegari - Mathematical Society of Japan
This is a comprehensive introduction to the theory of stable commutator length, an important subfield of quantitative topology, with substantial connections to 2-manifolds, dynamics, geometric group theory, bounded cohomology, symplectic topology.
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.
by Daniel Dugger - University of Oregon
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.