Torus link homology and the nabla operator

JOURNAL OF COMBINATORIAL THEORY SERIES A

卷:154

Article

Wilson, A. T.¹ 

[1] Univ Penn, Dept Math, Philadelphia, PA 19104 USA

关键词: Torus links;    Khovanov-Rozansky homology;    Macdonald polynomials;    Macdonald eigenoperators;    Nabla operator;   

DOI  :  10.1016/j.jcta.2017.08.009

来源: Elsevier

【 摘 要 】

In recent work, Elias and Hogancamp develop a recurrence for the Poincare series of the triply graded Khovanov-Rozansky homology of certain links, one of which is the (n, n) torus link. In this case, Elias and Hogancamp give a combinatorial formula for this homology that is reminiscent of the combine, torics of the modified Macdonald polynomial eigenoperator del. We give a combinatorial formula for the homologies of all complexes considered by Elias and Hogancamp. Our first formula is not easily computable, so we show how to transform it into a computable version. Finally, we conjecture a direct relationship between the (n, n) torus link case of our formula and the symmetric function del p(1)(n). Published by Elsevier Inc.

【 授权许可】

Free