Legendrian DGA Representations and the Colored Kauffman Polynomial

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2020
• Main Authors: Murray, Justin, Rutherford, Dan
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2020
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/210593
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: Legendrian DGA Representations and the Colored Kauffman Polynomial. Justin Murray and Dan Rutherford. SIGMA 16 (2020), 017, 33 pages

For any Legendrian knot 𝛫 in standard contact ℝ³, we relate counts of ungraded (1-graded) representations of the Legendrian contact homology DG-algebra (A(𝛫), ∂) with the n-colored Kauffman polynomial. To do this, we introduce an ungraded n-colored ruling polynomial, R¹ₙ, 𝛫(q), as a linear combinati...