An Introduction To Manifolds (universitext)
by Loring W. Tu /
2007 / English / PDF
5.6 MB Download
In this streamlined introduction to the subject, the theory of
manifolds is presented with the aim of helping the reader achieve a
rapid mastery of the essential topics. By the end of the book the
reader should be able to compute, at least for simple spaces, one
of the most basic topological invariants of a manifold, its de Rham
cohomology. Along the way the reader acquires the knowledge and
skills necessary for further study of geometry and topology. The
requisite point-set topology is included in an appendix of twenty
pages, while other appendices review facts from real analysis and
linear algebra. Hints and solutions are provided to many of the
exercises and problems.
In this streamlined introduction to the subject, the theory of
manifolds is presented with the aim of helping the reader achieve a
rapid mastery of the essential topics. By the end of the book the
reader should be able to compute, at least for simple spaces, one
of the most basic topological invariants of a manifold, its de Rham
cohomology. Along the way the reader acquires the knowledge and
skills necessary for further study of geometry and topology. The
requisite point-set topology is included in an appendix of twenty
pages, while other appendices review facts from real analysis and
linear algebra. Hints and solutions are provided to many of the
exercises and problems.
