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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This volume concerns spectra with enriched multiplicative structure. It is a truism that interesting cohomology theories are represented by ring spectra, the product on the spectrum giving rise to the cup products in the theory.
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Contents: Topological and Metric Spaces, Homotopy Exquivalence, Fundamental Groups, Covering Spaces and Applications, Classification of Surfaces, Simplicial Complexes and Homology Groups, Homology Calculations, Simplicial Approximation, etc.
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In this book the authors present the technical tools needed for proving rigorously the classification theorem, give a detailed proof using these tools, and also discuss the history of the theorem and its various proofs.