Chapter 1
Preliminaries
The last thing one knows in constructing a work is what to put
first
Blaise Pascal, Pensees
The first chapter contains a fast and unavoidable biased survey of some
basic facts needed in understanding Seiberg-Witten theory. The choices in
this minimal review reflect the author's background and taste and may not
answer everyone's needs. We hope the generous list of references will more
than make up for the various omissions.
This introductory chapter has only one goal, namely to familiarize the
reader with the basic terms and points of view in the Seiberg-Witten world
and cannot serve as a substitute for a solid background.
1.1. Bundles, connections and characteristic
classes
1.1.1. Vector bundles and connections. Smooth vector bundles for-
malize the notion of "smooth family of vector spaces". For example, given
a smooth manifold M and a vector space F we can think of the Cartesian
product
F = FM := F x M
1
http://dx.doi.org/10.1090/gsm/028/01
Previous Page Next Page