Notes on the Atiyah-Singer Index Theorem
by Liviu I. Nicolaescu
Publisher: University of Notre Dame 2005
Number of pages: 135
This is arguably one of the deepest and most beautiful results in modern geometry, and it is surely a must know for any geometer / topologist. It has to do with elliptic partial differential operators on a compact manifold.
Home page url
Download or read it online for free here:
by Bianca Santoro - arXiv
The author aimed at providing a first introduction to the main general ideas on the study of the Ricci flow, as well as guiding the reader through the steps of Kaehler geometry for the understanding of the complex version of the Ricci flow.
by 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.
by Alexander I. Bobenko (ed.) - Springer
This is the book on a newly emerging field of discrete differential geometry. It surveys the fascinating connections between discrete models in differential geometry and complex analysis, integrable systems and applications in computer graphics.
by Peter W. Michor - Universitaet Wien
Gauge theory usually investigates the space of principal connections on a principal fiber bundle (P,p,M,G) and its orbit space under the action of the gauge group (called the moduli space), which is the group of all principal bundle automorphisms...