Universal Khovanov-Rozansky sl(2) cohomology
Carmen Caprau
TL;DR
This paper develops a universal version of Khovanov-Rozansky sl(2) cohomology using a two-parameter potential, unifying existing foam and cohomology theories in link invariants.
Contribution
It introduces a universal Khovanov-Rozansky sl(2) cohomology theory parameterized by two variables, extending previous models.
Findings
Equivalence with universal foam sl(2) link cohomology after tensoring with suitable rings
Generalization of the cohomology for n=2 using a two-parameter potential
Unification of different sl(2) link homology theories
Abstract
We generalize the Khovanov-Rozansky cohomology for n=2 by means of a homogeneous potential that depends on two parameters, to obtain the universal Khovanov-Rozansky sl(2) link cohomology. This theory is equivalent to the universal foam sl(2) link cohomology, after tensoring both theories with appropriate rings.
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Taxonomy
TopicsGeometric and Algebraic Topology · Homotopy and Cohomology in Algebraic Topology · Advanced Combinatorial Mathematics