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.
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by Anders Kock - University of Aarhus
This textbook can be used as a non-technical and geometric gateway to many aspects of differential geometry. The audience of the book is anybody with a reasonable mathematical maturity, who wants to learn some differential geometry.
by Joseph M. Landsberg - arXiv
Homogeneous varieties, Topology and consequences Projective differential invariants, Varieties with degenerate Gauss images, Dual varieties, Linear systems of bounded and constant rank, Secant and tangential varieties, and more.
by Paul Loya - Binghamton University
This is a lecture-based class on the Atiyah-Singer index theorem, proved in the 60's by Sir Michael Atiyah and Isadore Singer. Their work on this theorem lead to a joint Abel prize in 2004. Requirements: Knowledge of topology and manifolds.
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...