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Introduction to Geometry and Topology (Compact Textbooks in Mathematics) by Werner Ballmann; Walker Stern; Springer Basel AG is a nonfiction available to read on EtoBox.

What is Introduction to Geometry and Topology (Compact Textbooks in Mathematics) about?

This book provides an introduction to topology, differential topology, and differential geometry. It is based on manuscripts refined through use in a variety of lecture courses. The first chapter covers elementary results and concepts from point-set topology. An exception is the Jordan Curve Theorem, which is proved for polygonal paths and is intended to give students a first glimpse into the nature of deeper topological problems. The second chapter of the book introduces manifolds and Lie groups, and examines a wide assortment of examples. Further discussion explores tangent bundles, vector bundles, differentials, vector fields, and Lie brackets of vector fields. This discussion is deepened and expanded in the third chapter, which introduces the de Rham cohomology and the oriented integral and gives proofs of the Brouwer Fixed-Point Theorem, the Jordan-Brouwer Separation Theorem, and Stokes's integral formula. The fourth and final chapter is devoted to the fundamentals of differential geometry and traces the development of ideas from curves to submanifolds of Euclidean spaces. Along the way, the book discusses connections and curvature--the central concepts of differential geometr

Who reads Introduction to Geometry and Topology (Compact Textbooks in Mathematics)?

Author

Werner Ballmann; Walker Stern; Springer Basel AG

Publisher

Springer Basel;Birkhäuser

Published

2018

Language

EN

ISBN

9783034809009

Category

nonfiction

Subjects

Mathematics, Geometry And Topology, Stem