Morse Homology

Schwarz (Autor)

Buch | Softcover

IX, 236 Seiten

2012
Springer Basel (Verlag)
978-3-0348-9688-7 (ISBN)

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1.1 Background The subject of this book is Morse homology as a combination of relative Morse theory and Conley's continuation principle. The latter will be useda s an instrument to express the homology encoded in a Morse complex associated to a fixed Morse function independent of this function. Originally, this type of Morse-theoretical tool was developed by Andreas Floer in order to find a proof of the famous Arnold conjecture, whereas classical Morse theory turned out to fail in the infinite-dimensional setting. In this framework, the homological variant of Morse theory is also known as Floer homology. This kind of homology theory is the central topic of this book. But first, it seems worthwhile to outline the standard Morse theory. 1.1.1 Classical Morse Theory The fact that Morse theory can be formulated in a homological way is by no means a new idea. The reader is referred to the excellent survey paper by Raoul Bott [Bol.

1 Introduction.- 1.1 Background.- 1.2 Overview.- 1.3 Remarks on the Methods.- 1.4 Table of Contents.- 1.5 Acknowledgments.- 2 The Trajectory Spaces.- 2.1 The Construction of the Trajectory Spaces.- 2.2 Fredholm Theory.- 2.3 Transversality.- 2.4 Compactness.- 2.5 Gluing.- 3 Orientation.- 3.1 Orientation and Gluing in the Trivial Case.- 3.2 Coherent Orientation.- 4 Morse Homology Theory.- 4.1 The Main Theorems of Morse Homology.- 4.2 The Eilenberg-Steenrod Axioms.- 4.3 The Uniqueness Result.- 5 Extensions.- 5.1 Morse Cohomology.- 5.2 Poincaré Duality.- 5.3 Products.- A Curve Spaces and Banach Bundles.- B The Geometric Boundary Operator.

"The proofs are written with great care, and Schwarz motivates all ideas with great skill...This is an excellent book."
- Bulletin of the AMS

Erscheint lt. Verlag	8.10.2012
Reihe/Serie	Progress in Mathematics
Zusatzinfo	IX, 236 p.
Verlagsort	Basel
Sprache	englisch
Maße	155 x 235 mm
Gewicht	391 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Analysis
Themenwelt	Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
Schlagworte	Analysis • Calculus • Finite • Function • Geometry • manifold • Morphism • Proof • Theorem • Topology
ISBN-10	3-0348-9688-3 / 3034896883
ISBN-13	978-3-0348-9688-7 / 9783034896887
Zustand	Neuware