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Introduction to commutative algebra
* Introduction * Rings and Ideals * Modules * Rings and Modules of Fractions * Primary Decomposition * Integral Dependence and Valuations * Chain Conditions * Noetherian Rings * Artin Rings *
The Yang-Mills equations over Riemann surfaces
  • M. Atiyah, R. Bott
  • Mathematics
    Philosophical Transactions of the Royal Society…
  • 1983
The Yang-Mills functional over a Riemann surface is studied from the point of view of Morse theory. The main result is that this is a ‘perfect' functional provided due account is taken of its gauge
Spectral Asymmetry and Riemannian Geometry
This has an analytic continuation to the whole s-plane as a meromorphic function of 5 and s = 0 is not a pole: moreover CA(o) can be computed as an explicit integral over the manifold [9]. In this
Spectral asymmetry and Riemannian geometry I
1. Introduction . The main purpose of this paper is to present a generalization of Hirzebruch's signature theorem for the case of manifolds with boundary. Our result is in the framework of Riemannian
Vector Bundles Over an Elliptic Curve
Introduction THE primary purpose of this paper is the study of algebraic vector bundles over an elliptic curve (defined over an algebraically closed field k). The interest of the elliptic curve lies
Self-duality in four-dimensional Riemannian geometry
We present a self-contained account of the ideas of R. Penrose connecting four-dimensional Riemannian geometry with three-dimensional complex analysis. In particular we apply this to the self-dual
The Geometry and Dynamics of Magnetic Monopoles
Systems governed by non-linear differential equations are of fundamental importance in all branches of science, but our understanding of them is still extremely limited. In this book a particular
Convexity and Commuting Hamiltonians
The converse was proved by A. Horn [5], so that all points in this convex hull occur as diagonals of some matrix A with the given eigenvalues. Kostant [7] generalized these results to any compact Lie