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Basic Algebraic Topology (Hardcover, New)
Loot Price: R3,293
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Basic Algebraic Topology (Hardcover, New)
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Building on rudimentary knowledge of real analysis, point-set
topology, and basic algebra, Basic Algebraic Topology provides
plenty of material for a two-semester course in algebraic topology.
The book first introduces the necessary fundamental concepts, such
as relative homotopy, fibrations and cofibrations, category theory,
cell complexes, and simplicial complexes. It then focuses on the
fundamental group, covering spaces and elementary aspects of
homology theory. It presents the central objects of study in
topology visualization: manifolds. After developing the homology
theory with coefficients, homology of the products, and cohomology
algebra, the book returns to the study of manifolds, discussing
Poincare duality and the De Rham theorem. A brief introduction to
cohomology of sheaves and Cech cohomology follows. The core of the
text covers higher homotopy groups, Hurewicz's isomorphism theorem,
obstruction theory, Eilenberg-Mac Lane spaces, and Moore-Postnikov
decomposition. The author then relates the homology of the total
space of a fibration to that of the base and the fiber, with
applications to characteristic classes and vector bundles. The book
concludes with the basic theory of spectral sequences and several
applications, including Serre's seminal work on higher homotopy
groups. Thoroughly classroom-tested, this self-contained text takes
students all the way to becoming algebraic topologists. Historical
remarks throughout the text make the subject more meaningful to
students. Also suitable for researchers, the book provides
references for further reading, presents full proofs of all
results, and includes numerous exercises of varying levels.
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