Differential Topology

e-books in Differential Topology category

Contact Topology
by George Torres, Robert Gompf - University of Texas at Austin , 2017
This is a course on contact manifolds, which are odd dimensional manifolds with an extra structure called a contact structure. Most of our study will focus on three dimensional manifolds, though many of these notions hold for any odd dimension.
(4549 views)

Differential Topology
by Bjorn Ian Dundas - Johns Hopkins University , 2002
This is an elementary text book for the civil engineering students with no prior background in point-set topology. This is a rather terse mathematical text, but provided with an abundant supply of examples and exercises with hints.
(11020 views)

Differential Topology and Morse Theory
by Dirk Schuetz - University of Sheffield , 2009
These notes describe basic material about smooth manifolds (vector fields, flows, tangent bundle, partitions of unity, Whitney embedding theorem, foliations, etc...), introduction to Morse theory, and various applications.
(11188 views)

Differential Topology of Fiber Bundles
by Karl-Hermann Neeb - FAU Erlangen-Nuernberg , 2010
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.
(10126 views)

Introduction to Differential Topology, de Rham Theory and Morse Theory
by Michael Muger - Radboud University , 2005
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.
(12181 views)

Introduction to Differential Topology
by Uwe Kaiser - Boise State University , 2006
This is a preliminary version of introductory lecture notes for Differential Topology. We try to give a deeper account of basic ideas of differential topology than usual in introductory texts. Many examples of manifolds are worked out in detail.
(10115 views)

Contact Geometry
by Hansjoerg Geiges - arXiv , 2004
This is an introductory text on the more topological aspects of contact geometry. After discussing some of the fundamental results of contact topology, I move on to a detailed exposition of the original proof of the Lutz-Martinet theorem.
(11768 views)

Ricci Flow and the Poincare Conjecture
by John Morgan, Gang Tian - American Mathematical Society , 2007
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.
(13388 views)

Lecture Notes on Differentiable Manifolds
by Jie Wu - National University of Singapore , 2004
Contents: Tangent Spaces, Vector Fields in Rn and the Inverse Mapping Theorem; Topological and Differentiable Manifolds, Diffeomorphisms, Immersions, Submersions and Submanifolds; Examples of Manifolds; Fibre Bundles and Vector Bundles; etc.
(12320 views)

Tight and Taut Submanifolds
by Thomas E. Cecil, Shiing-shen Chern - Cambridge University Press , 1997
Tight and taut submanifolds form an important class of manifolds with special curvature properties, one that has been studied intensively by differential geometers since the 1950's. This book contains six articles by leading experts in the field.
(12006 views)

Introduction to Symplectic and Hamiltonian Geometry
by Ana Cannas da Silva , 2007
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.
(14697 views)

Manifolds of Differentiable Mappings
by Peter W. Michor - Birkhauser , 1980
This book is devoted to the theory of manifolds of differentiable mappings and contains result which can be proved without the help of a hard implicit function theorem of nuclear function spaces. All the necessary background is developed in detail.
(10699 views)

Lectures on Symplectic Geometry
by Ana Cannas da Silva - Springer , 2006
An introduction to symplectic geometry and topology, it provides a useful and effective synopsis of the basics of symplectic geometry and serves as the springboard for a prospective researcher. The text is written in a clear, easy-to-follow style.
(15158 views)

Symplectic Geometry
by Ana Cannas da Silva - Princeton University , 2004
An overview of symplectic geometry – the geometry of symplectic manifolds. From a language of classical mechanics, symplectic geometry became a central branch of differential geometry and topology. This survey gives a partial flavor on this field.
(12888 views)

Differentiable Manifolds
by Nigel Hitchin , 2003
The historical driving force of the theory of manifolds was General Relativity, where the manifold is four-dimensional spacetime, wormholes and all. This text is occupied with the theory of differential forms and the exterior derivative.
(19173 views)