Algebraic & Geometric Topology

A trivial tail homology for non-$A$–adequate links

Christine Ruey Shan Lee

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We prove a conjecture of Rozansky’s concerning his categorification of the tail of the colored Jones polynomial for an A –adequate link. We show that the tail homology groups he constructs are trivial for non- A –adequate links.

Article information

Algebr. Geom. Topol., Volume 18, Number 3 (2018), 1481-1513.

Received: 6 January 2017
Revised: 20 September 2017
Accepted: 27 September 2017
First available in Project Euclid: 26 April 2018

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 57M25: Knots and links in $S^3$ {For higher dimensions, see 57Q45} 57M27: Invariants of knots and 3-manifolds

categorification colored Khovanov homology Jones polynomial


Lee, Christine Ruey Shan. A trivial tail homology for non-$A$–adequate links. Algebr. Geom. Topol. 18 (2018), no. 3, 1481--1513. doi:10.2140/agt.2018.18.1481.

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  • C Armond, The head and tail conjecture for alternating knots, Algebr. Geom. Topol. 13 (2013) 2809–2826
  • C Armond, O T Dasbach, Rogers–Ramanujan type identities and the head and tail of the colored Jones polynomial, preprint (2011)
  • D Bar-Natan, Khovanov's homology for tangles and cobordisms, Geom. Topol. 9 (2005) 1443–1499
  • B Cooper, V Krushkal, Categorification of the Jones–Wenzl projectors, Quantum Topol. 3 (2012) 139–180
  • F Costantino, Integrality of Kauffman brackets of trivalent graphs, Quantum Topol. 5 (2014) 143–184
  • O T Dasbach, X-S Lin, On the head and the tail of the colored Jones polynomial, Compos. Math. 142 (2006) 1332–1342
  • I Frenkel, M Khovanov, C Stroppel, A categorification of finite-dimensional irreducible representations of quantum $\mathfrak{sl}_2$ and their tensor products, Selecta Math. 12 (2006) 379–431
  • S Garoufalidis, T T Q Lê, Nahm sums, stability and the colored Jones polynomial, Res. Math. Sci. 2 (2015) art. id. 1
  • C R S Lee, Stability properties of the colored Jones polynomial, preprint (2014)
  • C R S Lee, R van der Veen, Slopes for pretzel knots, New York J. Math. 22 (2016) 1339–1364
  • W B R Lickorish, An introduction to knot theory, Graduate Texts in Mathematics 175, Springer (1997)
  • W B R Lickorish, M B Thistlethwaite, Some links with nontrivial polynomials and their crossing-numbers, Comment. Math. Helv. 63 (1988) 527–539
  • N Y Reshetikhin, V G Turaev, Ribbon graphs and their invariants derived from quantum groups, Comm. Math. Phys. 127 (1990) 1–26
  • L Rozansky, An infinite torus braid yields a categorified Jones–Wenzl projector, Fund. Math. 225 (2014) 305–326
  • L Rozansky, Khovanov homology of a unicolored B-adequate link has a tail, Quantum Topol. 5 (2014) 541–579
  • H Wenzl, On sequences of projections, C. R. Math. Rep. Acad. Sci. Canada 9 (1987) 5–9
  • S Yamada, A topological invariant of spatial regular graphs, from “Knots 90” (A Kawauchi, editor), de Gruyter, Berlin (1992) 447–454