Introduction to Geometry and Topology
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The work Introduction to Geometry and Topology represents a distinct intellectual or artistic creation found in Boston University Libraries. This resource is a combination of several types including: Work, Language Material, Books.
The Resource
Introduction to Geometry and Topology
Resource Information
The work Introduction to Geometry and Topology represents a distinct intellectual or artistic creation found in Boston University Libraries. This resource is a combination of several types including: Work, Language Material, Books.
 Label
 Introduction to Geometry and Topology
 Statement of responsibility
 by Werner Ballmann
 Subject

 Global Analysis and Analysis on Manifolds
 Global analysis (Mathematics)
 Global analysis (Mathematics)
 Manifolds (Mathematics)
 Manifolds (Mathematics)
 Manifolds (Mathematics)
 Manifolds and Cell Complexes (incl. Diff.Topology)
 Mathematics
 Mathematics
 Complex manifolds
 Complex manifolds
 Differential Geometry
 Electronic resources
 Geometry, Differential
 Geometry, Differential
 Language
 eng
 Summary
 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 pointset 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 FixedPoint Theorem, the JordanBrouwer 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 curvaturethe 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 twosemester bachelor's course
 Image bit depth
 0
 LC call number

 QA613613.8
 QA613.6613.66
 Literary form
 non fiction
 Series statement
 Compact Textbooks in Mathematics,
Context
Context of Introduction to Geometry and TopologyWork of
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