Floer Homology Groups in Yang-Mills Theory (Cambridge Tracts in Mathematics)
Contributors: M. Furuta (Assistant); D. Kotschick (Assistant)
Publisher: Cambridge University Press
Published: February 11, 2002
Language: eng
Format: Hardcover
Number of pages: 244
ISBN-13: 9780521808033
Subjects: Algebraic topology; Applied mathematics; Geometry; Yang-Mills theory; Mathematics; Differential Geometry; Quantum Field Theory; Science; Science/Mathematics; Geometry - Differential; Mathematics / Applied; Geometry - Algebraic; Quantum Theory; Geometry, Differential
First sentence: In 1985 Andreas Floer discovered new topological invariants of certain 3-manifolds, the 'Floer homology groups'.
Description: The concept of Floer homology was one of the most striking developments in differential geometry. It yields rigorously defined invariants which can be viewed as homology groups of infinite-dimensional cycles. The ideas led to great advances in the areas of low-dimensional topology and symplectic geometry and are intimately related to developments in Quantum Field Theory. The first half of this book gives a thorough account of Floer's construction in the context of gauge theory over 3 and 4-dimensional manifolds. The second half works out some further technical developments of the theory, and the final chapter outlines some research developments for the future - including a discussion of the appearance of modular forms in the theory. The scope of the material in this book means that it will appeal to graduate students as well as those on the frontiers of the subject.