Differential Algebraic Topology: From Stratifolds to Exotic Spheres (Graduate Studies in Mathematics) 1st Edition by Matthias Kreck (PDF)

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This book presents a geometric introduction to the homology of topological spaces and the cohomology of smooth manifolds. The author introduces a new class of stratified spaces, so-called stratifolds. He derives basic concepts from differential topology such as Sard’s theorem, partitions of unity and transversality. Based on this, homology groups are constructed in the framework of stratifolds and the homology axioms are proved. This implies that for nice spaces these homology groups agree with ordinary singular homology. Besides the standard computations of homology groups using the axioms, straightforward constructions of important homology classes are given. The author also defines stratifold cohomology groups following an idea of Quillen. Again, certain important cohomology classes occur very naturally in this description, for example, the characteristic classes which are constructed in the book and applied later on. One of the most fundamental results, Poincare duality, is almost

User’s Reviews

Editorial Reviews: Review “Differential Algebraic Topology: From Stratifolds to Exotic Spheres is a good book. It is clearly written, has many good examples and illustrations, and, as befits a graduate-level text, exercises. It is a wonderful addition to the literature.” —- MAA Reviews”This book is a very nice addition to the existing books on algebraic topology. A careful effort has been made to give the intuitive background when a new concept is introduced. This and the choice of topics makes reading the book a real pleasure.” —- Marko Kranjc, Mathematical Reviews

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