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• One of Bott's first insights was to see how to extend Morse theory to this situation.
• This became a starting point of the Morse theory which is now one of the basic parts of differential topology.
• Circle-valued Morse theory originated from a problem in hydrodynamics studied by S. P. Novikov in the early 1980s.
• Invented by Robin Forman in the mid 1990s, discrete Morse theory is a combinatorial analogue of Marston Morse's classical Morse theory.
• This book, the first one devoted solely to discrete Morse theory, serves as an introduction to the subject.
• This is the first time both smooth and discrete Morse theory have been treated in a single volume.
• This book could be a nice text for a course on Morse theory in a wide sense.
• Since then, great efforts have been made to extend the Morse theory.
• Nicolaescu’s book starts with the basics of Morse theory over the reals … .
• Before Morse, Arthur Cayley and James Clerk Maxwell had developed some of the ideas of Morse theory in the context of topography.
• A basic result of Morse theory says that almost all functions are Morse functions.
• Morse theory can be used to prove some strong results on the homology of manifolds.
• Morse theory has been used to classify closed 2-manifolds up to diffeomorphism.
• Novikov–Morse theory is a variant using multivalued functions.
• The basic results in global Morse theory are as follows.
• Its aim is to transfer the results of Morse theory 1 to this space (more correctly, to a suitable model of it).
• (implicitly) appear, therefore Morse theory establishes a connection between the curvature of a manifold and its topology.
• Morse theory was developed in the 1920s by mathematician Marston Morse.

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• ID : Q2296951