Elements of Differential Topology

Anant R. Shastri is a professor in the Department of Mathematics at the Indian Institute of Technology, Bombay. His research interests encompass topology and algebraic geometry.

… in Shastri’s treatment, the subject [differential forms] is developed in the larger context of the author’s stated goals, which makes for very good motivation and increased accessibility. Shastri does an excellent job with this foundational material. … It’s altogether a solid introduction to serious themes likely to persuade the reader to go deeper into the subject. Shastri’s exposition is rigorous at the same time that it evinces a light touch, and this of course makes for a very readable book. Examples abound, proofs are done in detail and include discussion along the lines of what one might hear in a good lecture presentation, and there are exercises replete with hints or solutions. Pedagogically, Elements of Differential Topology clearly gets very high marks. It is a good and useful textbook.—MAA Reviews, July 2011Professor Shastri’s book gives an excellent point of entry to this fascinating area of mathematics by providing the basic motivation and background needed for the study of differential geometry, algebraic topology, and Lie groups. … A major strength of Professor Shastri’s book is that detailed arguments are given in places where other books leave too much for the reader to supply on his/her own. This, together with the large quantity of accessible exercises, makes this book particularly reader friendly as a stable text for an introductory course in differential topology.—From the Foreword by F. Thomas Farrell, Binghamton, New York, USA

• Review of Differential Calculus. Integral Calculus. Submanifolds of Euclidean Spaces. Integration on Manifolds. Abstract Manifolds. Isotopy. Intersection Theory. Geometry of Manifolds. Lie Groups and Lie Algebras: The Basics. Hints/Solutions to Select Exercises. Bibliography. Index.