Read e-book online An Introduction to Manifolds (Universitext) PDF

By Loring W. Tu

Manifolds, the higher-dimensional analogs of gentle curves and surfaces, are basic gadgets in sleek 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 assisting the reader in achieving a speedy mastery of the fundamental issues. through the top of the booklet the reader may be capable of compute, at the least for easy areas, some of the most uncomplicated topological invariants of a manifold, its de Rham cohomology. alongside the best way, the reader acquires the data and talents useful for additional learn of geometry and topology. The considered necessary point-set topology is integrated in an appendix of twenty pages; different appendices assessment proof from actual research and linear algebra. tricks and suggestions are supplied to a few of the workouts and problems.

This paintings can be used because the textual content for a one-semester graduate or complex undergraduate direction, in addition to by way of scholars engaged in self-study. Requiring in simple terms minimum undergraduate must haves, 'Introduction to Manifolds' is usually a great origin 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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