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Sur l'homologie de Khovanov-Rozansky des graphes et des entrelacs.

Abstract : This thesis is devoted to the categorification of polynomial invariants of graphs and links. For any positive integer n, Khovanov and Rozansky introduced in 2004 a bigraded link homology, and an homology of planar graphs. Given n, their link homology categorifies the n-th specialization of the HOMFLY-PT polynomial and their homology of planar graphs categorifies an associated graph polynomial.

In this thesis, we study these homology and generalize their constructions by introducing an additional grading. First, we generalize a formula of Jaeger for link polynomials to polynomials of planar graphs and associated homology of planar graphs; we extend also the link homology of Khovanov and Rozansky to embedded graphs. Then we construct a triply graded link homology. This homology recovers the bigraded link homology of Khovanov and Rozansky. Finally, we give examples, applications and generalizations of the triply graded link homology. We develop homological tools that permit to compute explicitly the triply graded link homology for some knots and we consider deformations of the triply graded link homology.
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Contributor : Emmanuel Wagner <>
Submitted on : Wednesday, November 28, 2007 - 9:51:59 AM
Last modification on : Friday, June 19, 2020 - 9:10:04 AM
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  • HAL Id : tel-00192447, version 1



Emmanuel Wagner. Sur l'homologie de Khovanov-Rozansky des graphes et des entrelacs.. Mathematics [math]. Université Louis Pasteur - Strasbourg I, 2007. English. ⟨NNT : 2007STR13126⟩. ⟨tel-00192447⟩



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