Gauge Theory and Symplectic Geometry

1997
ISBN: 978-0-7923-4500-8
Verlag: Springer Netherlands

Buch, Englisch, 212 Seiten, Format (B × H): 160 mm x 241 mm, Gewicht: 1130 g

Reihe: Nato Science Series C:

Gauge theory, symplectic geometry and symplectic topology are important areas at the crossroads of several mathematical disciplines. The present book, with expertly written surveys of recent developments in these areas, includes some of the first expository material of Seiberg-Witten theory, which has revolutionised the subjects since its introduction in late 1994.
Topics covered include: introductions to Seiberg-Witten theory, to applications of the S-W theory to four-dimensional manifold topology, and to the classification of symplectic manifolds; an introduction to the theory of pseudo-holomorphic curves and to quantum cohomology; algebraically integrable Hamiltonian systems and moduli spaces; the stable topology of gauge theory, Morse-Floer theory; pseudo-convexity and its relations to symplectic geometry; generating functions; Frobenius manifolds and topological quantum field theory.

Zielgruppe

Research

Autoren/Hrsg.

Hurtubise, Jacques

Lalonde, François

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen
• Mathematik | Informatik Mathematik Geometrie Differentialgeometrie
• Mathematik | Informatik Mathematik Geometrie Nicht-Euklidische Geometrie
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
• Mathematik | Informatik Mathematik Topologie Algebraische Topologie
• Mathematik | Informatik Mathematik Mathematische Analysis Harmonische Analysis, Fourier-Mathematik

Inhaltsverzeichnis

Lectures on gauge theory and integrable systems.- Symplectic geometry of plurisubharmonic functions.- Frobenius manifolds.- Moduli spaces and particle spaces.- J-holomorphic curves and symplectic invariants.- Lectures on Gromov invariants for symplectic 4-manifolds.