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Analysis and Algebra on Differentiable Manifolds: A Workbook for Students and Teachers
Pedro M. Gadea, Jaime Muñoz Masqué, and Ihor V. Mykytyuk
Publisher: Springer (2013)Details: 617 pages, Hardcover
Edition: 2 Series: Problem Books in Mathematics
Price: $89.95
ISBN: 9789400759510
Category: Problem Book
Topics: Riemannian Geometry, Manifolds, Lie Groups, Geometric Analysis
MAA Review
[Reviewed by Fernando Q. Gouvêa, on 02/14/2013]See our review of the first edition. The new edition has an added author and is published in hard covers. The authors tell us that 39 problems have been deleted and 76 have been added. Other changes include:
- The Einstein summation convention is no longer used. (Hurray!)
- There is a section on what happens if one drops the standard topological assumptions (Hausdorff and second-countable) in the definition of a differentiable manifold.
- Several of the more advanced sections (on Lie groups, characteristic classes, connections) have been significantly expanded.
- A final chapter gives a collection of formulas and tables relevant to differential geometry.
This book is an excellent resource for teachers and students of these topics.