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A new structure on Khovanov's homology

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dc.contributor.advisor Tomasz S. Mrowka. en_US Lee, Eun Soo, 1975- en_US
dc.contributor.other Massachusetts Institute of Technology. Dept. of Mathematics. en_US 2005-05-19T15:13:50Z 2005-05-19T15:13:50Z 2003 en_US 2003 en_US
dc.description Thesis (Ph.D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2003. en_US
dc.description Includes bibliographical references (p. 49). en_US
dc.description This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections. en_US
dc.description.abstract The purpose of this thesis is proving conjectures in [1] on the Khovanov invariant. Khovanov invariant [6] is an invariant of (relatively) oriented links which is a cohomology theory over the cube of the resolutions of a link diagram. Khovanov invariant specializes to the Jones polynomial by taking graded Euler characteristic. Bar-Natan [1] [2] computed this invariant for the prime knots of up to 11 crossings. From the data, Bar-Natan, Garoufalidis, and Khovanov formulated two conjectures on the value of the Khovanov invariant of an alternating knot [1][4]. We prove those conjectures by constructing a new map on Khovanov's chain complex which, with the original coboundary map, gives rise to a double complex structure on the chain complex. en_US
dc.description.statementofresponsibility by Eun Soo Lee. en_US
dc.format.extent 49 p. en_US
dc.format.extent 693623 bytes
dc.format.extent 693384 bytes
dc.format.mimetype application/pdf
dc.format.mimetype application/pdf
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.subject Mathematics. en_US
dc.title A new structure on Khovanov's homology en_US
dc.type Thesis en_US Ph.D. en_US
dc.contributor.department Massachusetts Institute of Technology. Dept. of Mathematics. en_US
dc.identifier.oclc 52276222 en_US

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