A new structure on Khovanov's homology
Author(s)Lee, Eun Soo, 1975-
Massachusetts Institute of Technology. Dept. of Mathematics.
Tomasz S. Mrowka.
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The purpose of this thesis is proving conjectures in  on the Khovanov invariant. Khovanov invariant  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   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 . 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.
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.
DepartmentMassachusetts Institute of Technology. Dept. of Mathematics.
Massachusetts Institute of Technology