Floer Homology, Gauge Theory, and Low Dimensional Topology
by David Ellwood, at al.
Publisher: American Mathematical Society 2006
Number of pages: 314
Mathematical gauge theory studies connections on principal bundles, or, more precisely, the solution spaces of certain partial differential equations for such connections. Historically, these equations have come from mathematical physics, and play an important role in the description of the electro-weak and strong nuclear forces.
Download or read it online for free here:
by C. Nash - arXiv
In this essay we wish to embark on the telling of a story which, almost certainly, stands only at its beginning. We shall discuss the links and the interaction between one very old subject, physics, and a much newer one, topology.
by Andrew Ranicki - Cambridge University Press
Noncommutative localization is a technique for constructing new rings by inverting elements, matrices and more generally morphisms of modules. The applications to topology are via the noncommutative localizations of the fundamental group rings.
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.
by Reyer Sjamaar - Cornell University
The text covers manifolds and differential forms for an audience of undergraduates who have taken a typical calculus sequence, including basic linear algebra and multivariable calculus up to the integral theorems of Green, Gauss and Stokes.