Differential topology: first steps

By:

Wallace, Andrew

Series: Dover books on mathematicsPublication details: Dover Publications, 1996. Mineola:Description: xiii, 130 p.: ill.; pb; 22 cmISBN:

9780486453170

Subject(s):

DDC classification:

514.72 WAL

Summary: Keeping mathematical prerequisites to a minimum, this undergraduate-level text stimulates students' intuitive understanding of topology while avoiding the more difficult subtleties and technicalities. Its focus is the method of spherical modifications and the study of critical points of functions on manifolds.No previous knowledge of topology is necessary for this text, which offers introductory material regarding open and closed sets and continuous maps in the first chapter. Succeeding chapters discuss the notions of differentiable manifolds and maps and explore one of the central topics of differential topology, the theory of critical points of functions on a differentiable manifold. Additional topics include an investigation of level manifolds corresponding to a given function and the concept of spherical modifications. The text concludes with applications of previously discussed material to the classification problem of surfaces and guidance, along with suggestions for further reading and study.

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Holdings
Item type	Current library	Collection	Call number	Copy number	Status	Date due	Barcode
Books	IIT Gandhinagar General Stacks	General	514.72 WAL (Browse shelf(Opens below))	1	Available		029390

Includes bibliographical references (p. 127-128) and index.

Keeping mathematical prerequisites to a minimum, this undergraduate-level text stimulates students' intuitive understanding of topology while avoiding the more difficult subtleties and technicalities. Its focus is the method of spherical modifications and the study of critical points of functions on manifolds.No previous knowledge of topology is necessary for this text, which offers introductory material regarding open and closed sets and continuous maps in the first chapter. Succeeding chapters discuss the notions of differentiable manifolds and maps and explore one of the central topics of differential topology, the theory of critical points of functions on a differentiable manifold. Additional topics include an investigation of level manifolds corresponding to a given function and the concept of spherical modifications. The text concludes with applications of previously discussed material to the classification problem of surfaces and guidance, along with suggestions for further reading and study.

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