Morse Theory and Floer Homology
- 種類:
- 電子ブック
- 責任表示:
- by Michèle Audin, Mihai Damian
- 出版情報:
- London : Springer London : Imprint: Springer, 2014
- 著者名:
- シリーズ名:
- Universitext ;
- ISBN:
- 9781447154969 [1447154967]
- 注記:
- 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. The first part is a thorough introduction to Morse theory, a fundamental tool of differential topology. It defines the Morse complex and the Morse homology, and develops some of their applications. Morse homology also serves a simple model for Floer homology, which is covered in the second part. Floer homology is an infinite-dimensional analogue of Morse homology. Its involvement has been crucial in the recent achievements in symplectic geometry and in particular in the proof of the Arnold conjecture. The building blocks of Floer homology are more intricate and imply the use of more sophisticated analytical methods, all of which are explained
- ローカル注記:
- 岐阜大学構成員専用E-BOOKS (Gifu University members only)
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