2021/05/18 by Tushar Pandey, Pandey, Tushar, Ka Ho Wong +1
Biochemistry, Genetics and Molecular Biology · Mathematics · #57K10 #57K14 #57K31 #57K32 #Advanced Operator Algebra Research #Connective tissue disorders research #FOS: Mathematics #FOS: Physical sciences #Geometric Analysis and Curvature Flows #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Geometry and complex manifolds #Mathematical Physics (math-ph) #Quantum Algebra (math.QA)
paper · pdf · doi:10.48550/arxiv.2105.08805
openalex publication_date 2021/05/18 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28
We study the asymptotic expansion conjecture of the relative\nReshetikhin-Turaev invariants proposed in citeWY4 for all pairs (M,L)\nsatisfying the property that M\∖ L is homeomorphic to some fundamental\nshadow link complement. The hyperbolic cone structure of such (M,L) can be\ndescribed by using the logarithmic holonomies of the meridians of some\nfundamental shadow link. We show that when the logarithmic holonomies are\nsufficiently small and all cone angles are less than \π, the asymptotic\nexpansion conjecture of (M,L) is true. Especially, we verify the asymptotic\nexpansion conjecture of the relative Reshetikhin-Turaev invariants for all\npairs (M,L) satisfying the property that M\∖ L is homeomorphic to\nsome fundamental shadow link complement, with cone angles sufficiently small.\nFurthermore, we show that if M is obtained by doing rational surgery on a\nfundamental shadow link complement with sufficiently large surgery\ncoefficients, then the cone angles can be pushed to any value less than \π.\n