A simple proof of the strong integrality for full colored HOMFLYPT invariants
Shengmao Zhu
TL;DR
This paper provides a straightforward proof demonstrating the strong integrality property of reduced colored HOMFLYPT invariants within the framework of HOMFLY skein theory, enhancing understanding of their algebraic structure.
Contribution
It offers a simple proof of the strong integrality for full colored HOMFLYPT invariants using skein theory, clarifying their algebraic properties.
Findings
Proved strong integrality of reduced colored HOMFLYPT invariants
Utilized HOMFLY skein theory for the proof
Simplified understanding of algebraic structure of invariants
Abstract
By using the HOMFLY skein theory. We prove a strong integrality theorem for the reduced colored HOMFLYPT invariants defined by a basis in the full HOMFLY skein of the annulus.
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Taxonomy
TopicsGeometric and Algebraic Topology · Advanced Algebra and Geometry · Markov Chains and Monte Carlo Methods