Geodesic
THE CONORMAL TORUS IS A COMPLETE KNOT INVARIANT
Forum of Mathematics, Pi, Tome 7 (2019)

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We use microlocal sheaf theory to show that knots can only have Legendrian isotopic conormal tori if they themselves are isotopic or mirror images. 
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VIVEK SHENDE. THE CONORMAL TORUS IS A COMPLETE KNOT INVARIANT. Forum of Mathematics, Pi, Tome 7 (2019). doi: 10.1017/fmp.2019.1

[Abo] Abouzaid, M., ‘Nearby Lagrangians with vanishing Maslov class are homotopy equivalent’, Invent. Math. 189(2) (2012), 251–313.Google Scholar

[AK] Abouzaid, M. and Kragh, T., ‘Simple homotopy equivalence of nearby Lagrangians’, Acta Mathematica 220(2) (2018), 207–237.Google Scholar

[BBD] Beilinson, A., Bernstein, J. and Deligne, P., ‘Faisceaux pervers’, Astérisque 100 (1982), 5–171.Google Scholar

[BEY] Berest, Y., Eshmatov, A. and Yeung, W.-K., ‘Perverse sheaves and knot contact homology’, Comptes Rendus Mathematique 355(4) (2017), 378–399.Google Scholar

[BO] Bondal, A. and Orlov, D., ‘Reconstruction of a variety from the derived category and groups of autoequivalences’, Compositio Math. 125(3) (2001), 327–344.Google Scholar

[Bot] Bott, R., ‘On manifolds all of whose geodesics are closed’, Ann. of Math. (2) 60 (1954), 375–382.Google Scholar

[Chi] Chiu, S.-F., ‘Non-squeezing property of contact balls’, Duke Mathematical Journal 166(4) (2017), 605–655.Google Scholar

[CELN] Cieliebak, K., Ekholm, T., Latschev, J. and Ng, L., ‘Knot contact homology, string topology, and the cord algebra’, Journal de l’École polytechnique-Mathématiques 4 (2017), 661–780.Google Scholar

[Cor1] Cornwell, C. R., ‘KCH representations, augmentations, and A-polynomials’, Journal of Symplectic Geometry 15(4) (2017), 983–1017.Google Scholar

[Cor2] Cornwell, C. R., ‘Knot contact homology and representations of knot groups’, J. Topol. 7(4) (2014), 1221–1242.Google Scholar

[ENS] Ekholm, T., Ng, L. and Shende, V., ‘A complete knot invariant from contact homology’, Inventiones mathematicae 211(3) (2018), 1149–1200.Google Scholar

[FSS] Fukaya, K., Seidel, P. and Smith, I., ‘Exact Lagrangian submanifolds in simply-connected cotangent bundles’, Invent. Math. 172(1) (2008), 1–27.Google Scholar

[Gr] Gray, J., ‘Some global properties of Contact structures’, Ann. of Math. (2) 69(2) (1959), 421–450.Google Scholar

[GL] Gordon, C. and Luecke, J., ‘Knots are determined by their complements’, J. Amer. Math. Soc. 2(2) (1989), 371–415.Google Scholar

[GLi] Gordon, C. and Lidman, T., ‘Knot contact homology detects cabled, composite, and torus knots’, Proceedings of the American Mathematical Society 145(12) (2017), 5405–5412.Google Scholar

[Gui] Guillermou, S., ‘Quantization of conic Lagrangian submanifolds of cotangent bundles’. Preprint, 2012, arXiv:1212.5818.Google Scholar

[Gui2] Guillermou, S., ‘The Gromov–Eliashberg theorem by microlocal sheaf theory’. Preprint, 2013, arXiv:1311.0187.Google Scholar

[Gui3] Guillermou, S., ‘The three cusps conjecture’. Preprint, 2016, arXiv:1603.07876.Google Scholar

[GKS] Guillermou, S., Kashiwara, M. and Schapira, P., ‘Sheaf quantization of Hamiltonian isotopies and applications to nondisplaceability problems’, Duke Math. J. 161(2) (2012), 201–245.Google Scholar

[Her] Hertwick, M., ‘A counterexample to the isomorphism problem for integral group rings’, Ann. of Math. (2) 154(1) (2001), 115–138.Google Scholar

[Hig] Higman, G., ‘The units of group-rings’, Proc. Lond. Math. Soc. (2) 46 (1940), 231–248.Google Scholar

[HS] Howie, J. and Short, H., ‘The band-sum problem’, J. Lond. Math. Soc. (2) 31(3) (1985), 571–576.Google Scholar

[KS] Kashiwara, M. and Schapira, P., Sheaves on Manifolds, Grundlehren Math. Wiss., 292 (Springer, 1990).Google Scholar

[N1] Nadler, D., ‘Microlocal branes are constructible sheaves’, Selecta Math. (N.S.) 15(4) (2009), 563–619.Google Scholar

[Ng3] Ng, L., ‘Framed knot contact homology’, Duke Math. J. 141(2) (2008), 365–406.Google Scholar

[Orl] Orlov, D., ‘Derived categories of coherent sheaves and equivalences between them’, Russian Math. Surveys 58(3) (2003), 511–591.Google Scholar

[STZ] Shende, V., Treumann, D. and Zaslow, E., ‘Legendrian knots and constructible sheaves’, Inventiones mathematicae 207(3) (2017), 1031–1133.Google Scholar

[STWZ] Shende, V., Treumann, D., Williams, H. and Zaslow, E., ‘Cluster varieties from Legendrian knots’. Duke Mathematical Journal, Preprint, 2015, arXiv:1512.08942, to appear.Google Scholar

[STW] Shende, V., Treumann, D. and Williams, H., ‘On the combinatorics of exact Lagrangian surfaces’. Preprint, 2016, arXiv:1603.07449.Google Scholar

[Tam] Tamarkin, D., ‘Microlocal condition for non-displaceablility’, inAlgebraic and Analytic Microlocal Analysis (Springer, 2013), 99–223.Google Scholar

[Wal] Waldhausen, F., ‘On irreducible 3-manifolds which are sufficiently large’, Ann. of Math. (2) 87(1) (1968), 56–88.Google Scholar

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