Quadratic Forms with Applications to Algebraic Geometry and Topology [Paperback]

A gem of a book bringing together 30 years worth of results that are certain to interest anyone whose research touches on quadratic forms.Bringing together thirty years' worth of results about quadratic forms, the topics in this collection include Hilbert's 17th problem, the Tsen-Lang theory of quasi-algebraically closed fields, the level of topological spaces, and systems of quadratic forms over arbitrary fields.Bringing together thirty years' worth of results about quadratic forms, the topics in this collection include Hilbert's 17th problem, the Tsen-Lang theory of quasi-algebraically closed fields, the level of topological spaces, and systems of quadratic forms over arbitrary fields.This volume discusses results about quadratic forms that give rise to interconnections among number theory, algebra, algebraic geometry, and topology. The author deals with various topics including Hilbert's 17th problem, the Tsen-Lang theory of quasi-algebraically closed fields, the level of topological spaces, and systems of quadratic forms over arbitrary fields. Whenever possible, proofs are short and elegant, and the author has made this book as self-contained as possible. This book brings together thirty years' worth of results certain to interest anyone whose research touches on quadratic forms.1. The representation theory of Cassels; 2. Multiplicative quadratic forms; 3. The level of fields, rings and topological spaces; 4. Hilbert's homogeneous nullstellensatz; 5. Tsen-Lang theory; 6. Hilbert's 17th problem; 7. The Pythagoras number; 8. The u-invariant; 9. Systems of quadratic forms; 10. The level of projective spaces.'A very readable complement to the standard treatments.' Mathematica