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Morse Theory and Floer Homology
ISBN-13:
9781447154969
Veröffentl:
2013
Seiten:
596
Autor:
Michèle Audin
Serie:
Universitext
eBook Typ:
PDF
eBook Format:
EPUB
Kopierschutz:
1 - PDF Watermark
Sprache:
Englisch
Beschreibung:
This book is an introduction to modern methods of symplectic topology. It is devoted to explaining the solution of an important problem originating from classical mechanics: the 'Arnold conjecture', which asserts that the number of 1-periodic trajectories of a non-degenerate Hamiltonian system is bounded below by the dimension of the homology of the underlying manifold.
Introduction to Part I.- Morse Functions.- Pseudo-Gradients.- The Morse Complex.- Morse Homology, Applications.- Introduction to Part II.- What You Need To Know About Symplectic Geometry.- The Arnold Conjecture and the Floer Equation.- The Maslov Index.- Linearization and Transversality.- Spaces of Trajectories.- From Floer To Morse.- Floer Homology: Invariance.- Elliptic Regularity.- Technical Lemmas.- Exercises for the Second Part.- Appendices: What You Need to Know to Read This Book.
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