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 gadgets in glossy arithmetic. Combining facets of algebra, topology, and research, manifolds have additionally been utilized to classical mechanics, normal relativity, and quantum box theory.

In this streamlined creation to the topic, the idea of manifolds is gifted with the purpose of assisting the reader in attaining a speedy mastery of the basic themes. by way of the tip of the e-book the reader can be capable of compute, not less than for easy areas, the most uncomplicated topological invariants of a manifold, its de Rham cohomology. alongside the best way, the reader acquires the information and abilities priceless for additional research of geometry and topology. The needful point-set topology is integrated in an appendix of twenty pages; different appendices overview evidence from genuine research and linear algebra. tricks and suggestions are supplied to some of the workouts 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 in simple terms minimum undergraduate necessities, 'Introduction to Manifolds' can be a very good origin for Springer's GTM eighty two, 'Differential varieties in Algebraic Topology'.

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