by Danny Calegari
Publisher: Mathematical Society of Japan 2009
Number of pages: 218
This book 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, and many other subjects.
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by Peter Petersen - UCLA
These notes are a supplement to a first year graduate course in manifold theory. These are the topics covered: Manifolds (Smooth Manifolds, Projective Space, Matrix Spaces); Basic Tensor Analysis; Basic Cohomology Theory; Characteristic Classes.
by Andrew Ranicki, Norman Levitt, Frank Quinn - Springer
The book present original research on a wide range of topics in modern topology: the algebraic K-theory of spaces, the algebraic obstructions to surgery and finiteness, geometric and chain complexes, characteristic classes, and transformation groups.
by Jacob Lurie - Princeton University Press
Jacob Lurie presents the foundations of higher category theory, using the language of weak Kan complexes, and shows how existing theorems in algebraic topology can be reformulated and generalized in the theory's new language.
by F. R. Cohen, T. J. Lada, P. J. May - Springer
A thorough treatment of homology operations and of their application to the calculation of the homologies of various spaces. The book studies an up to homotopy notion of an algebra over a monad and its role in the theory of iterated loop spaces.