Introduction to Geometry and Topology

Introduction to Geometry and Topology
Author :
Publisher : Birkhäuser
Total Pages : 174
Release :
ISBN-10 : 9783034809832
ISBN-13 : 3034809832
Rating : 4/5 (832 Downloads)

Book Synopsis Introduction to Geometry and Topology by : Werner Ballmann

Download or read book Introduction to Geometry and Topology written by Werner Ballmann and published by Birkhäuser. This book was released on 2018-07-18 with total page 174 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 geometry. The discussion culminates with the Gauß equations and the version of Gauß's theorema egregium for submanifolds of arbitrary dimension and codimension. This book is primarily aimed at advanced undergraduates in mathematics and physics and is intended as the template for a one- or two-semester bachelor's course.


Introduction to Geometry and Topology Related Books

Introduction to Geometry and Topology
Language: en
Pages: 174
Authors: Werner Ballmann
Categories: Mathematics
Type: BOOK - Published: 2018-07-18 - Publisher: Birkhäuser

GET EBOOK

This book provides an introduction to topology, differential topology, and differential geometry. It is based on manuscripts refined through use in a variety of
Introduction to Topology and Geometry
Language: en
Pages: 430
Authors: Saul Stahl
Categories: Mathematics
Type: BOOK - Published: 2014-08-21 - Publisher: John Wiley & Sons

GET EBOOK

An easily accessible introduction to over three centuries of innovations in geometry Praise for the First Edition “. . . a welcome alternative to compartmenta
Geometry with an Introduction to Cosmic Topology
Language: en
Pages: 255
Authors: Michael P. Hitchman
Categories: Mathematics
Type: BOOK - Published: 2009 - Publisher: Jones & Bartlett Learning

GET EBOOK

The content of Geometry with an Introduction to Cosmic Topology is motivated by questions that have ignited the imagination of stargazers since antiquity. What
Geometry and Topology of Manifolds: Surfaces and Beyond
Language: en
Pages: 420
Authors: Vicente Muñoz
Categories: Education
Type: BOOK - Published: 2020-10-21 - Publisher: American Mathematical Soc.

GET EBOOK

This book represents a novel approach to differential topology. Its main focus is to give a comprehensive introduction to the classification of manifolds, with
Knots, Molecules, and the Universe
Language: en
Pages: 406
Authors: Erica Flapan
Categories: Mathematics
Type: BOOK - Published: 2015-12-22 - Publisher: American Mathematical Soc.

GET EBOOK

This book is an elementary introduction to geometric topology and its applications to chemistry, molecular biology, and cosmology. It does not assume any mathem