Floer-Novikov cohomology and its applications
Floer (co) -homology is an infinite dimensional analog of classical Morse (co) -homology, changing the gradient equation of the Morse function f by the gradient of the action functional A defined in the contractible loop space. This change implied that the objects that make up the moduli space of bo...
- Autores:
-
Gómez Cobos, David Santiago
- Tipo de recurso:
- Fecha de publicación:
- 2020
- Institución:
- Universidad de los Andes
- Repositorio:
- Séneca: repositorio Uniandes
- Idioma:
- eng
- OAI Identifier:
- oai:repositorio.uniandes.edu.co:1992/50823
- Acceso en línea:
- http://hdl.handle.net/1992/50823
- Palabra clave:
- Teoría homológica
Conjetura de Novikov
Homología de Floer
Matemáticas
- Rights
- openAccess
- License
- http://creativecommons.org/licenses/by-nc-sa/4.0/
| Summary: | Floer (co) -homology is an infinite dimensional analog of classical Morse (co) -homology, changing the gradient equation of the Morse function f by the gradient of the action functional A defined in the contractible loop space. This change implied that the objects that make up the moduli space of bounded gradient lines were of different nature. Floer found that an appropriate way to deal with these objects was the theory of pseudo-holomorphic curves developed by Gromov. The incorporation of this theory presented some problems for the compactness and transversality of the moduli space in question, specifically the appearance of unwanted pseudo-holomorphic spheres in sequences of pseudo-holomorphic curves. Floer solved these problems by imposing a condition of monotonicity on the manifold (M, w), causing his proof of Arnold's conjecture to be not general. The purpose of this document is to present the details of the construction of a more general Floer (co) -homology (Floer-Novikov cohomology)... |
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