February 2016
Beginner
551 pages
19h 3m
English
Content preview from Basic Algebraic Topology
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Foreword
While the subject of algebraic topology began long before H. Poincaré’s Analysis Situs, the discipline started to take shape only in the 1930s during which the foundation of modern algebraic topology was laid. Fundamental concepts such as manifolds, fiber spaces, higher homotopy groups, and various homology and cohomology theories were firmly established. Meanwhile, obstruction theory, cohomology operations, and spectral sequences were among some of the powerful tools developed as the subject rapidly grew. By the 1960s (see [Dieudonné, 1989]), algebraic topology was already a well-established discipline and together with differential topology dominated much of mathematics at the time.
Applications to analysis and other fields were some ...
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