Ricci Flow and the Poincare Conjecture
by John Morgan, Gang Tian
Publisher: American Mathematical Society 2007
Number of pages: 493
This book provides full details of a complete proof of the Poincare Conjecture following Grigory Perelman's three preprints. With the large amount of background material that is presented and the detailed versions of the central arguments, this book is suitable for all mathematicians from advanced graduate students to specialists in geometry and topology.
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by J.L. Koszul - Tata Institute of Fundamental Research
From the table of contents: Differential Calculus; Differentiable Bundles; Connections on Principal Bundles; Holonomy Groups; Vector Bundles and Derivation Laws; Holomorphic Connections (Complex vector bundles, Almost complex manifolds, etc.).
by Dave Auckly - arXiv
This paper introduced undergraduates to the Atiyah-Singer index theorem. It includes a statement of the theorem, an outline of the easy part of the heat equation proof. It includes counting lattice points and knot concordance as applications.
by Peter J. Cameron - Queen Mary College
The author is concerned with the geometry of incidence of points and lines, over an arbitrary field, and unencumbered by metrics or continuity (or even betweenness). The treatment of these themes blends the descriptive with the axiomatic.
by Andreas Kriegl, Peter W. Michor - American Mathematical Society
This book lays the foundations of differential calculus in infinite dimensions and discusses those applications in infinite dimensional differential geometry and global analysis not involving Sobolev completions and fixed point theory.