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- One of Bott's first insights was to see how to extend Morse theory to this situation.[1]
- This became a starting point of the Morse theory which is now one of the basic parts of differential topology.[2]
- Circle-valued Morse theory originated from a problem in hydrodynamics studied by S. P. Novikov in the early 1980s.[2]
- Invented by Robin Forman in the mid 1990s, discrete Morse theory is a combinatorial analogue of Marston Morse's classical Morse theory.[3]
- This book, the first one devoted solely to discrete Morse theory, serves as an introduction to the subject.[3]
- This is the first time both smooth and discrete Morse theory have been treated in a single volume.[4]
- This book could be a nice text for a course on Morse theory in a wide sense.[4]
- Since then, great efforts have been made to extend the Morse theory.[5]
- Nicolaescu’s book starts with the basics of Morse theory over the reals … .[6]
- Before Morse, Arthur Cayley and James Clerk Maxwell had developed some of the ideas of Morse theory in the context of topography.[7]
- A basic result of Morse theory says that almost all functions are Morse functions.[7]
- Morse theory can be used to prove some strong results on the homology of manifolds.[7]
- Morse theory has been used to classify closed 2-manifolds up to diffeomorphism.[7]
- Novikov–Morse theory is a variant using multivalued functions.[8]
- The basic results in global Morse theory are as follows.[9]
- Its aim is to transfer the results of Morse theory 1 to this space (more correctly, to a suitable model of it).[9]
- (implicitly) appear, therefore Morse theory establishes a connection between the curvature of a manifold and its topology.[9]
- Morse theory was developed in the 1920s by mathematician Marston Morse.[10]
소스
- ↑ Morse theory
- ↑ 2.0 2.1 Circle-valued Morse Theory
- ↑ 3.0 3.1 Discrete Morse Theory
- ↑ 4.0 4.1 Morse Theory
- ↑ Morse Theory in Differential Equations
- ↑ An Invitation to Morse Theory
- ↑ 7.0 7.1 7.2 7.3 Morse theory
- ↑ Morse theory in nLab
- ↑ 9.0 9.1 9.2 Encyclopedia of Mathematics
- ↑ Morse Theory. (AM-51), Volume 51
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- ID : Q2296951
Spacy 패턴 목록
- [{'LOWER': 'morse'}, {'LEMMA': 'theory'}]