A universal U(1)-RCC invariant of links and rationality conjecture
L. Rozansky
TL;DR
This paper introduces a universal U(1)-RCC invariant for links in rational homology spheres, derived via a graph algebra approach, and proposes a conjecture on its rationality structure.
Contribution
It develops a graph algebra framework for the stationary phase integration in link invariants and defines a universal invariant that encompasses simpler Lie algebra invariants.
Findings
Defines a graph algebra version of stationary phase integration
Constructs a universal U(1)-RCC invariant for links
Proposes a rationality conjecture for the invariant's structure
Abstract
We define a graph algebra version of the stationary phase integration over the coadjoint orbits in the Reshetikhin formula for the colored Jones-HOMFLY polynomial. As a result, we obtain a `universal' U(1)-RCC invariant of links in rational homology spheres, which determines the U(1)-RCC invariants based on simple Lie algebras. We formulate a rationality conjecture about the structure of this invariant.
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Taxonomy
TopicsGeometric and Algebraic Topology · Homotopy and Cohomology in Algebraic Topology · Advanced Combinatorial Mathematics