Low Dimensional Geometry and Topology Special Feature: Tour of bordered Floer theory
Heegaard Floer theory is a kind of topological quantum field theory (TQFT), assigning graded groups to closed, connected, oriented 3-manifolds and group homomorphisms to smooth, oriented four-dimensional cobordisms. Bordered Heegaard Floer homology is an extension of Heegaard Floer homology to 3-man...
| Main Authors: | , , |
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| Other Authors: | |
| Format: | Article |
| Language: | en_US |
| Published: |
National Academy of Sciences (U.S.)
2013
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| Online Access: | http://hdl.handle.net/1721.1/80705 |
| _version_ | 1811083708660187136 |
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| author | Ozsvath, Peter Lipshitz, Robert Thurston, Dylan P. |
| author2 | Massachusetts Institute of Technology. Department of Mathematics |
| author_facet | Massachusetts Institute of Technology. Department of Mathematics Ozsvath, Peter Lipshitz, Robert Thurston, Dylan P. |
| author_sort | Ozsvath, Peter |
| collection | MIT |
| description | Heegaard Floer theory is a kind of topological quantum field theory (TQFT), assigning graded groups to closed, connected, oriented 3-manifolds and group homomorphisms to smooth, oriented four-dimensional cobordisms. Bordered Heegaard Floer homology is an extension of Heegaard Floer homology to 3-manifolds with boundary, with extended-TQFT-type gluing properties. In this survey, we explain the formal structure and construction of bordered Floer homology and sketch how it can be used to compute some aspects of Heegaard Floer theory. |
| first_indexed | 2024-09-23T12:37:51Z |
| format | Article |
| id | mit-1721.1/80705 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T12:37:51Z |
| publishDate | 2013 |
| publisher | National Academy of Sciences (U.S.) |
| record_format | dspace |
| spelling | mit-1721.1/807052022-10-01T10:08:59Z Low Dimensional Geometry and Topology Special Feature: Tour of bordered Floer theory Tour of bordered Floer theory Ozsvath, Peter Lipshitz, Robert Thurston, Dylan P. Massachusetts Institute of Technology. Department of Mathematics Ozsvath, Peter Heegaard Floer theory is a kind of topological quantum field theory (TQFT), assigning graded groups to closed, connected, oriented 3-manifolds and group homomorphisms to smooth, oriented four-dimensional cobordisms. Bordered Heegaard Floer homology is an extension of Heegaard Floer homology to 3-manifolds with boundary, with extended-TQFT-type gluing properties. In this survey, we explain the formal structure and construction of bordered Floer homology and sketch how it can be used to compute some aspects of Heegaard Floer theory. National Science Foundation (U.S.) (Grant DMS-0505811) 2013-09-13T12:35:45Z 2013-09-13T12:35:45Z 2011-04 2010-12 Article http://purl.org/eprint/type/JournalArticle 0027-8424 1091-6490 http://hdl.handle.net/1721.1/80705 Lipshitz, R., P. S. Ozsvath, and D. P. Thurston. “Low Dimensional Geometry and Topology Special Feature: Tour of bordered Floer theory.” Proceedings of the National Academy of Sciences 108, no. 20 (May 17, 2011): 8085-8092. en_US http://dx.doi.org/10.1073/pnas.1019060108 Proceedings of the National Academy of Sciences Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. application/pdf National Academy of Sciences (U.S.) PNAS |
| spellingShingle | Ozsvath, Peter Lipshitz, Robert Thurston, Dylan P. Low Dimensional Geometry and Topology Special Feature: Tour of bordered Floer theory |
| title | Low Dimensional Geometry and Topology Special Feature: Tour of bordered Floer theory |
| title_full | Low Dimensional Geometry and Topology Special Feature: Tour of bordered Floer theory |
| title_fullStr | Low Dimensional Geometry and Topology Special Feature: Tour of bordered Floer theory |
| title_full_unstemmed | Low Dimensional Geometry and Topology Special Feature: Tour of bordered Floer theory |
| title_short | Low Dimensional Geometry and Topology Special Feature: Tour of bordered Floer theory |
| title_sort | low dimensional geometry and topology special feature tour of bordered floer theory |
| url | http://hdl.handle.net/1721.1/80705 |
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