Generalized Manifolds

1. Auflage 1997
ISBN: 978-0-582-32000-0
Verlag: Chapman and Hall/CRC

Buch, Englisch, Band 372, 128 Seiten, Format (B × H): 169 mm x 245 mm, Gewicht: 227 g

Reihe: Chapman & Hall/CRC Research Notes in Mathematics Series

In this Research Note, a generalization of the subject of differential geometry is developed, using techniques and results of nonstandard analysis. This generalization is found to correspond to approximations of classical manifolds by set-theoretic near manifold structures. Schlesinger develops several applications of the theory in the fields of topological dynamical systems, the question of stability of geodesic incompleteness (which is relevant to the problem of singularities in general relativity) and the deformation theory of manifolds. In the latter case, deformations induced by first cohomology can be introduced without encountering the restriction to compact manifolds as in the case of classical Kodaira-Spencer theory. This new deformation theory is then applied to a problem in twistor theory, thereby achieving a generalization of the nonlinear graviton construction of Penrose.

Autoren/Hrsg.

Schlesinger, Karl-Georg

Schlesinger, K G

Fachgebiete

• Mathematik | Informatik Mathematik Topologie Mengentheoretische Topologie
• Mathematik | Informatik Mathematik Mathematische Analysis
• Mathematik | Informatik Mathematik Geometrie Differentialgeometrie

Inhaltsverzeichnis

Introduction
The Case of Nonstandard Analogs of Compact Submanifolds of Rn
The General Nonstandard Manifold Concept
Some Applications to Nonstandard Topological Dynamics
The Cohomology Group H1(M,O)

The Question of Stability of Geodesic Incompleteness
An Application to Twistor Theory
A Physical Epilogue
List of Symbols
Bibliography
Index