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Mapping Degree Theory (Hardcover, New ed.)
Loot Price: R2,348
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Mapping Degree Theory (Hardcover, New ed.)
Series: Graduate Studies in Mathematics
Expected to ship within 10 - 15 working days
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This textbook treats the classical parts of mapping degree theory,
with a detailed account of its history traced back to the first
half of the 18th century. After a historical first chapter, the
remaining four chapters develop the mathematics. An effort is made
to use only elementary methods, resulting in a self-contained
presentation. Even so, the book arrives at some truly outstanding
theorems: the classification of homotopy classes for spheres and
the Poincare-Hopf Index Theorem, as well as the proofs of the
original formulations by Cauchy, Poincare, and others. Although the
mapping degree theory you will discover in this book is a classical
subject, the treatment is refreshing for its simple and direct
style. The straightforward exposition is accented by the appearance
of several uncommon topics: tubular neighborhoods without metrics,
differences between class 1 and class 2 mappings, Jordan Separation
with neither compactness nor cohomology, explicit constructions of
homotopy classes of spheres, and the direct computation of the Hopf
invariant of the first Hopf fibration. The book is suitable for a
one-semester graduate course. There are 180 exercises and problems
of different scope and difficulty.
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