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

By Loring W. Tu

Manifolds, the higher-dimensional analogs of delicate curves and surfaces, are basic items in smooth arithmetic. Combining features of algebra, topology, and research, manifolds have additionally been utilized to classical mechanics, basic 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 attaining a speedy mastery of the fundamental subject matters. via the tip of the e-book the reader may be in a position to compute, no less than for easy areas, probably the most uncomplicated topological invariants of a manifold, its de Rham cohomology. alongside the way in which, the reader acquires the information and talents worthwhile for extra research of geometry and topology. The needful point-set topology is incorporated in an appendix of twenty pages; different appendices evaluation evidence from actual research and linear algebra. tricks and ideas are supplied to a number of the workouts and problems.

This paintings can be used because the textual content for a one-semester graduate or complicated undergraduate path, in addition to through scholars engaged in self-study. Requiring in basic terms minimum undergraduate necessities, 'Introduction to Manifolds' can also be an outstanding beginning for Springer's GTM eighty two, 'Differential types in Algebraic Topology'.

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