2008/07/16 by Pedro Vaz, Vaz, Pedro · 1 citation
Mathematics · #Algebraic structures and combinatorial models #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Quantum Algebra (math.QA) #math.GT #math.QA
paper · pdf · doi:10.48550/arxiv.0807.2658
PhD thesis, 141 pages, lots of figures
arxiv created 2008/07/16 · openalex publication_date 2008/07/16 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
In this thesis we define and study a categorification of the sl(N)-link polynomial using foams, for N≥ 3. For N=3 we define the universal sl(3)-link homology, using foams, which depends on three parameters and show that it is functorial, up to scalars, with respect to link cobordisms. Our theory is integral. We show that tensoring it with Q yields a theory which is equivalent to the rational universal Khovanov-Rozansky sl(3)-link homology. For N≥ 4 we construct a rational theory categorifying the sl(N)-link polynomial using foams. Our theory is functorial, up to scalars, with respect to link cobordisms. To evaluate closed foams we use the Kapustin-Li formula. We show that for any link our homology is isomorphic to the Khovanov-Rozansky homology. We conjecture that the theory is integral and we compute the conjectured integral sl(N)-link homology for the (2,m)-torus links and show that it has torsion of order N.