An introduction to manifolds
Tu, Loring W.
An introduction to manifolds / by Loring W. Tu - 2nd ed. - New Delhi : Springer India Private Limited, 2012, 2011c. - 410 p. ill. ; 23 cm.
Include bibliography references and index
A Brief Introduction.- Part I. The Euclidean Space.- Smooth Functions on R(N).- Tangent Vectors In R(N) as Derivations.- Alternating K-Linear Functions.- Differential Forms on R(N).- Part II. Manifolds.- Manifolds.- Smooth Maps on A Manifold.- Quotient.- Part III. The Tangent Space.- The Tangent Space.- Submanifolds.- Categories And Functors.- The Image of A Smooth Map.- The Tangent Bundle.- Bump Functions and Partitions of Unity.- Vector Fields.- Part IV. Lie Groups and Lie Algebras.- Lie Groups.- Lie Algebras.- Part V. Differential Forms.- Differential 1-Forms.- Differential K-Forms.- The Exterior Derivative.- Part VI. Integration.- Orientations.- Manifolds With Boundary.- Integration on A Manifold.- Part VII. De Rham Theory.- De Rham Cohomology.- The Long Exact Sequence in Cohomology.- The Mayer-Vietoris Sequence.- Homotopy Invariance.- Computation of De Rham Cohomology.- Proof of Homotopy Invariance.- Appendix A. Point-Set Topology.- Appendix B. Inverse Function Theorem of R(N) And Related Results.- Appendix C. Existence of A Partition of Unity in General.- Appendix D. Solutions to Selected Exercises.- Bibliography.- Index.
"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
9781441973993 9781441974006
Manifolds --Mathematics
516.07 / TU-I 2012 261
An introduction to manifolds / by Loring W. Tu - 2nd ed. - New Delhi : Springer India Private Limited, 2012, 2011c. - 410 p. ill. ; 23 cm.
Include bibliography references and index
A Brief Introduction.- Part I. The Euclidean Space.- Smooth Functions on R(N).- Tangent Vectors In R(N) as Derivations.- Alternating K-Linear Functions.- Differential Forms on R(N).- Part II. Manifolds.- Manifolds.- Smooth Maps on A Manifold.- Quotient.- Part III. The Tangent Space.- The Tangent Space.- Submanifolds.- Categories And Functors.- The Image of A Smooth Map.- The Tangent Bundle.- Bump Functions and Partitions of Unity.- Vector Fields.- Part IV. Lie Groups and Lie Algebras.- Lie Groups.- Lie Algebras.- Part V. Differential Forms.- Differential 1-Forms.- Differential K-Forms.- The Exterior Derivative.- Part VI. Integration.- Orientations.- Manifolds With Boundary.- Integration on A Manifold.- Part VII. De Rham Theory.- De Rham Cohomology.- The Long Exact Sequence in Cohomology.- The Mayer-Vietoris Sequence.- Homotopy Invariance.- Computation of De Rham Cohomology.- Proof of Homotopy Invariance.- Appendix A. Point-Set Topology.- Appendix B. Inverse Function Theorem of R(N) And Related Results.- Appendix C. Existence of A Partition of Unity in General.- Appendix D. Solutions to Selected Exercises.- Bibliography.- Index.
"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
9781441973993 9781441974006
Manifolds --Mathematics
516.07 / TU-I 2012 261