Thesis (Ph.D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2003. / Includes bibliographical references (p. 49). / This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections. / 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. / by Eun Soo Lee. / Ph.D.
| Identifer | oai:union.ndltd.org:MIT/oai:dspace.mit.edu:1721.1/16904 |
| Date | January 2003 |
| Creators | Lee, Eun Soo, 1975- |
| Contributors | Tomasz S. Mrowka., Massachusetts Institute of Technology. Dept. of Mathematics., Massachusetts Institute of Technology. Dept. of Mathematics. |
| Publisher | Massachusetts Institute of Technology |
| Source Sets | M.I.T. Theses and Dissertation |
| Language | English |
| Detected Language | English |
| Type | Thesis |
| Format | 49 p., 693623 bytes, 693384 bytes, application/pdf, application/pdf, application/pdf |
| 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., http://dspace.mit.edu/handle/1721.1/7582 |
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