An Introduction to Manifolds (Universitext) by Loring W. Tu PDF

By Loring W. Tu

Manifolds, the higher-dimensional analogs of soft curves and surfaces, are primary items in sleek arithmetic. Combining points of algebra, topology, and research, manifolds have additionally been utilized to classical mechanics, common relativity, and quantum box theory.

In this streamlined creation to the topic, the speculation of manifolds is gifted with the purpose of aiding the reader in achieving a swift mastery of the basic themes. through the top of the booklet the reader will be in a position to compute, no less than for easy areas, some of the most easy topological invariants of a manifold, its de Rham cohomology. alongside the best way, the reader acquires the data and abilities priceless for extra research of geometry and topology. The considered necessary point-set topology is integrated in an appendix of twenty pages; different appendices evaluate evidence from actual research and linear algebra. tricks and suggestions are supplied to a number of the routines and problems.

This paintings can be used because the textual content for a one-semester graduate or complicated undergraduate direction, in addition to by way of scholars engaged in self-study. Requiring basically minimum undergraduate must haves, 'Introduction to Manifolds' is usually a very good starting place for Springer's GTM eighty two, 'Differential kinds in Algebraic Topology'.

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An Introduction to Manifolds (Universitext) by Loring W. Tu

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