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

By Loring W. Tu

Manifolds, the higher-dimensional analogs of tender curves and surfaces, are primary gadgets in sleek arithmetic. Combining elements 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 speculation of manifolds is gifted with the purpose of aiding the reader in attaining a quick mastery of the fundamental subject matters. through the tip of the booklet the reader may be in a position to compute, not less than for easy areas, essentially the most uncomplicated topological invariants of a manifold, its de Rham cohomology. alongside the best way, the reader acquires the information and talents beneficial for additional learn of geometry and topology. The needful point-set topology is incorporated in an appendix of twenty pages; different appendices assessment evidence from genuine research and linear algebra. tricks and options are supplied to a number of the routines and problems.

This paintings can be utilized because the textual content for a one-semester graduate or complex undergraduate path, in addition to by way of scholars engaged in self-study. Requiring merely minimum undergraduate must haves, 'Introduction to Manifolds' is additionally a good beginning for Springer's GTM eighty two, 'Differential kinds in Algebraic Topology'.

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