dc.contributor.advisor | Tomasz Mrowka. | en_US |
dc.contributor.author | Lipyanskiy, Maksim | en_US |
dc.contributor.other | Massachusetts Institute of Technology. Dept. of Mathematics. | en_US |
dc.date.accessioned | 2008-12-11T18:27:15Z | |
dc.date.available | 2008-12-11T18:27:15Z | |
dc.date.copyright | 2008 | en_US |
dc.date.issued | 2008 | en_US |
dc.identifier.uri | http://hdl.handle.net/1721.1/43785 | |
dc.description | Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2008. | en_US |
dc.description | Includes bibliographical references (p. 81-82). | en_US |
dc.description.abstract | This dissertation is concerned with the foundations of a new approach to Floer theory. As opposed to the traditional approach, which can be viewed as a generalization of Morse theory to an infinite dimensional setting, our approach is a generalization of bordism to infinite dimensions. The key new insight, based on unpublished work of Tom Mrowka and Peter Ozsvath, is an understanding of how to axiomatize compactness in the infinite dimensional setting. We describe a general axiomatic framework for setting up a Floer theory of a polarized Hilbert space equipped with a functional. The resulting bordism theory can be seen as a refinement of the traditional Floer theory. By introducing cycles with corners, we demonstrate how the bordism theory leads to a geometric description of homology. We relate our geometric construction to the Morse-theoretic approach by indicating how one might compute the Floer homology of the space, if the associated functional is Morse. The general theory is illustrated in two examples: Seiberg-Witten-Floer homology and symplectic Floer theory for loops in Cn. We end by indicating various generalizations of the theory. | en_US |
dc.description.statementofresponsibility | by Maksim Lipyanskiy. | en_US |
dc.format.extent | 82 p. | en_US |
dc.language.iso | eng | en_US |
dc.publisher | Massachusetts Institute of Technology | en_US |
dc.rights | M.I.T. theses are protected by
copyright. They may be viewed from this source for any purpose, but
reproduction or distribution in any format is prohibited without written
permission. See provided URL for inquiries about permission. | en_US |
dc.rights.uri | http://dspace.mit.edu/handle/1721.1/7582 | en_US |
dc.subject | Mathematics. | en_US |
dc.title | A semi-infinite cycle construction of Floer homology | en_US |
dc.type | Thesis | en_US |
dc.description.degree | Ph.D. | en_US |
dc.contributor.department | Massachusetts Institute of Technology. Department of Mathematics | |
dc.identifier.oclc | 261137861 | en_US |