| A Short Course in Differential Topology Contributor(s): Dundas, Bjørn Ian (Author) |
|
 |
ISBN: 1108425798 ISBN-13: 9781108425797 Publisher: Cambridge University Press OUR PRICE: $57.94 Product Type: Hardcover - Other Formats Published: August 2018 |
| Additional Information |
| BISAC Categories: - Mathematics | Topology - General |
| Dewey: 514.72 |
| LCCN: 2017061465 |
| Series: Cambridge Mathematical Textbooks |
| Physical Information: 0.69" H x 7.24" W x 10.26" (1.54 lbs) 262 pages |
| Descriptions, Reviews, Etc. |
| Publisher Description: Manifolds are abound in mathematics and physics, and increasingly in cybernetics and visualization where they often reflect properties of complex systems and their configurations. Differential topology gives us the tools to study these spaces and extract information about the underlying systems. This book offers a concise and modern introduction to the core topics of differential topology for advanced undergraduates and beginning graduate students. It covers the basics on smooth manifolds and their tangent spaces before moving on to regular values and transversality, smooth flows and differential equations on manifolds, and the theory of vector bundles and locally trivial fibrations. The final chapter gives examples of local-to-global properties, a short introduction to Morse theory and a proof of Ehresmann's fibration theorem. The treatment is hands-on, including many concrete examples and exercises woven into the text, with hints provided to guide the student. |