2014/10/08 by Qingtao Chen, Chen, Qingtao, Shengmao Zhu +1 · 1 citation
Mathematics · Physics and Astronomy · #57M25 #57M27 and 81R50 #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #FOS: Mathematics #FOS: Physical sciences #Geometric Topology (math.GT) #Geometric and Algebraic Topology #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Quantum Algebra (math.QA) #hep-th #math-ph #math.GT #math.MP #math.QA #msc:57M25 #msc:57M27 #msc:81R50
paper · pdf · doi:10.48550/arxiv.1410.2211
27 pages, 3 figures
arxiv created 2014/10/08 · openalex publication_date 2014/10/08 · arxiv updated 2014/10/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we investigate the properties of the full colored HOMFLYPT invariants in the full skein of the annulus C. We show that the full colored HOMFLYPT invariant has a nice structure when q→ 1. The composite invariant is a combination of the full colored HOMFLYPT invariants. In order to study the framed LMOV type conjecture for composite invariants, we introduce the framed reformulated composite invariant \checkRp(L). By using the HOMFLY skein theory, we prove that \checkRp(L) lies in the ring 2ℤ[(q-q-1)2,t± 1]. Furthermore, we propose a conjecture of congruent skein relation for \checkRp(L) and prove it for certain special cases.