
Triangles, Rotation, a Theorem and the Jackpot
by Dave Auckly
Publisher: arXiv 2013
Number of pages: 43
Description:
This is an expository paper designed to introduce undergraduates to the Atiyah-Singer index theorem 50 years after its announcement. It includes motivation, 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.
Download or read it online for free here:
Download link
(2.1MB, PDF)
Similar books
Lectures on Exterior Differential Systemsby M. Kuranishi - Tata Institute of Fundamental Research
Contents: Parametrization of sets of integral submanifolds (Regular linear maps, Germs of submanifolds of a manifold); Exterior differential systems (Differential systems with independent variables); Prolongation of Exterior Differential Systems.
(14489 views)
The Theory of Lie Derivatives and Its Applicationsby Kentaro Yano - North Holland Publishing Co.
The topics include: Spaces with a non-vanishing curvature tensor that admit a group of automorphisms of the maximum order; Groups of transformations in generalized spaces; Global properties of the groups of motions in a compact Riemannian space...
(5549 views)
Exterior Differential Systems and Euler-Lagrange Partial Differential Equationsby R. Bryant, P. Griffiths, D. Grossman - University Of Chicago Press
The authors present the results of their development of a theory of the geometry of differential equations, focusing especially on Lagrangians and Poincare-Cartan forms. They also cover certain aspects of the theory of exterior differential systems.
(19661 views)
Notes on Symmetric Spacesby Jonathan Holland, Bogdan Ion - arXiv
Contents: Affine connections and transformations; Symmetric spaces; Orthogonal symmetric Lie algebras; Examples; Noncompact symmetric spaces; Compact semisimple Lie groups; Hermitian symmetric spaces; Classification of real simple Lie algebras.
(11263 views)