Titlebook: An Invitation to Morse Theory; Liviu Nicolaescu Textbook 20071st edition Springer-Verlag New York 2007 Algebraic topology.Topology.algebra

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The Topology of Morse Functions,parameter . varies in an interval containing only regular values of a smooth function .: . → ?, then the topology of the sublevel set . ≤ . is independent of .. We can turn this on its head and state that a change in the topology of . ≤ . is an indicator of the presence of a critical point.

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https://doi.org/10.1007/978-3-476-04207-1parameter . varies in an interval containing only regular values of a smooth function .: . → ?, then the topology of the sublevel set . ≤ . is independent of .. We can turn this on its head and state that a change in the topology of . ≤ . is an indicator of the presence of a critical point.

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Die internen Gesetze im VertriebIn this first chapter we introduce the reader to the main characters of our story, namely the Morse functions, and we describe the properties which make them so useful. We describe their very special local structure (Morse lemma) and then we show that there are plenty of them around.

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Basics of Complex Morse Theory,In this final chapter we would like to introduce the reader to the complex version of Morse theory that has proved to be very useful in the study of the topology of complex projective varieties, and more recently in the study of the topology of symplectic manifolds.

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