Lectures on Differential Topology
by Riccardo Benedetti
Publisher: arXiv.org 2019
Number of pages: 416
Description:
This text is a comprehensive introduction to the theory of smooth manifolds, maps, and fundamental associated structures. It covers advanced topics such as degree theory, the Poincare-Hopf index theorem, bordism-characteristic numbers, and the Pontryagin-Thom construction. This book is suitable for beginning master's and doctoral students who have completed an undergraduate mathematics curriculum.
Download or read it online for free here:
Download link
(2.7MB, PDF)
Similar books
Introduction to Symplectic and Hamiltonian Geometryby Ana Cannas da Silva
The text covers foundations of symplectic geometry in a modern language. It describes symplectic manifolds and their transformations, and explains connections to topology and other geometries. It also covers hamiltonian fields and hamiltonian actions.
(15231 views)
Differential Topology of Fiber Bundlesby Karl-Hermann Neeb - FAU Erlangen-Nuernberg
From the table of contents: Basic Concepts (The concept of a fiber bundle, Coverings, Morphisms...); Bundles and Cocycles; Cohomology of Lie Algebras; Smooth G-valued Functions; Connections on Principal Bundles; Curvature; Perspectives.
(10655 views)
Introduction to Differential Topology, de Rham Theory and Morse Theoryby Michael Muger - Radboud University
Contents: Why Differential Topology? Basics of Differentiable Manifolds; Local structure of smooth maps; Transversality Theory; More General Theory; Differential Forms and de Rham Theory; Tensors and some Riemannian Geometry; Morse Theory; etc.
(12675 views)
Ricci Flow and the Poincare Conjectureby John Morgan, Gang Tian - American Mathematical Society
This book provides full details of a complete proof of the Poincare Conjecture following Grigory Perelman's preprints. The book is suitable for all mathematicians from advanced graduate students to specialists in geometry and topology.
(14083 views)