Curved Rickard complexes and link homologies

References

[1] M. T. Abram, L. Lamberto-Egan, A. D. Lauda and D. E. V. Rose, A categorification of the internal braid group action on quantum groups I: 2-functoriality, in preparation. Search in Google Scholar

[2] M. T. Abram, L. Lamberto-Egan, A. D. Lauda and D. E. V. Rose, A categorification of the internal braid group action on quantum groups II: Compatibility with Rickard complexes, in preparation. Search in Google Scholar

[3] J. Batson and C. Seed, A link-splitting spectral sequence in Khovanov homology, Duke Math. J. 164 (2015), no. 5, 801–841. 10.1215/00127094-2881374Search in Google Scholar

[4] A. Beliakova, K. Habiro, A. D. Lauda and B. Webster, Cyclicity for categorified quantum groups, J. Algebra 452 (2016), 118–132. 10.1016/j.jalgebra.2015.11.041Search in Google Scholar

[5] J. Brundan, On the definition of Kac–Moody 2-category, Math. Ann. 364 (2016), no. 1–2, 353–372. 10.1007/s00208-015-1207-ySearch in Google Scholar

[6] J. Brundan and C. Stroppel, Highest weight categories arising from Khovanov’s diagram algebra III: category 𝒪, Represent. Theory 15 (2011), 170–243. 10.1090/S1088-4165-2011-00389-7Search in Google Scholar

[7] S. Cautis, Rigidity in higher representation theory, preprint (2014), http://arxiv.org/abs/1409.0827. Search in Google Scholar

[8] S. Cautis, Clasp technology to knot homology via the affine Grassmannian, Math. Ann. 363 (2015), no. 3–4, 1053–1115. 10.1007/s00208-015-1196-xSearch in Google Scholar

[9] S. Cautis, Remarks on coloured triply graded link invariants, Algebr. Geom. Topol. 17 (2017), no. 6, 3811–3836. 10.2140/agt.2017.17.3811Search in Google Scholar

[10] S. Cautis and J. Kamnitzer, Knot homology via derived categories of coherent sheaves. I. The 𝔰⁢𝔩⁢(2)-case, Duke Math. J. 142 (2008), no. 3, 511–588. 10.1007/s00222-008-0138-6Search in Google Scholar

[11] S. Cautis and J. Kamnitzer, Braiding via geometric Lie algebra actions, Compos. Math. 148 (2012), no. 2, 464–506. 10.1112/S0010437X1100724XSearch in Google Scholar

[12] S. Cautis and J. Kamnitzer, Knot homology via derived categories of coherent sheaves IV, coloured links, Quantum Topol. 8 (2017), no. 2, 381–411. 10.4171/QT/93Search in Google Scholar

[13] S. Cautis, J. Kamnitzer and A. Licata, Categorical geometric skew Howe duality, Invent. Math. 180 (2010), no. 1, 111–159. 10.1007/s00222-009-0227-1Search in Google Scholar

[14] S. Cautis and A. D. Lauda, Implicit structure in 2-representations of quantum groups, Selecta Math. (N. S.) 21 (2015), no. 1, 201–244. 10.1007/s00029-014-0162-xSearch in Google Scholar

[15] J. Chuang and R. Rouquier, Derived equivalences for symmetric groups and 𝔰⁢𝔩2-categorification, Ann. of Math. (2) 167 (2008), no. 1, 245–298. 10.4007/annals.2008.167.245Search in Google Scholar

[16] B. Elias and M. Hogancamp, On the computation of torus link homology, Compos. Math. 155 (2019), no. 1, 164–205. 10.1112/S0010437X18007571Search in Google Scholar

[17] E. Gorsky and M. Hogancamp, Hilbert schemes and y-ification of Khovanov–Rozansky homology, preprint (2017), https://arxiv.org/pdf/math/1712.03938. 10.2140/gt.2022.26.587Search in Google Scholar

[18] E. Gorsky, A. Negut and J. Rasmussen, Flag Hilbert schemes, colored projectors and Khovanov–Rozansky homology, preprint (2016), http://arxiv.org/abs/arXiv:1608.07308. 10.1016/j.aim.2020.107542Search in Google Scholar

[19] M. Hogancamp, Khovanov–Rozansky homology and higher Catalan sequences, preprint (2017), https://arxiv.org/abs/1704.01562. Search in Google Scholar

[20] D. Huybrechts and R. P. Thomas, Deformation-obstruction theory for complexes via Atiyah and Kodaira–Spencer classes, Math. Ann. 346 (2010), no. 3, 545–569. 10.1007/s00208-009-0397-6Search in Google Scholar

[21] M. Khovanov and A. D. Lauda, A diagrammatic approach to categorification of quantum groups III, Quantum Topol. 1 (2010), no. 1, 1–92. 10.4171/QT/1Search in Google Scholar

[22] M. Khovanov, A. D. Lauda, M. Mackaay and M. Stošić, Extended graphical calculus for categorified quantum sl⁢(2), Mem. Amer. Math. Soc. 1029 (2012), 1–87. 10.1090/S0065-9266-2012-00665-4Search in Google Scholar

[23] P. B. Kronheimer and T. S. Mrowka, Gauge theory for embedded surfaces. I, Topology 32 (1993), no. 4, 773–826. 10.1016/0040-9383(93)90051-VSearch in Google Scholar

[24] P. B. Kronheimer and T. S. Mrowka, Khovanov homology is an unknot-detector, Publ. Math. Inst. Hautes Études Sci. 113 (2011), 97–208. 10.1007/s10240-010-0030-ySearch in Google Scholar

[25] A. D. Lauda, Categorified quantum sl⁢(2) and equivariant cohomology of iterated flag varieties, Algebr. Represent. Theory 14 (2011), no. 2, 253–282. 10.1007/s10468-009-9188-8Search in Google Scholar

[26] A. D. Lauda, Parameters in categorified quantum groups, preprint (2018), http://arxiv.org/abs/1812.07654. 10.1007/s10468-019-09890-8Search in Google Scholar

[27] E. S. Lee, The support of the Khovanov’s invariant for alternating knots, preprint (2002), http://arxiv.org/abs/0201105. Search in Google Scholar

[28] E. S. Lee, An endomorphism of the Khovanov invariant, Adv. Math. 197 (2005), no. 2, 554–586. 10.1016/j.aim.2004.10.015Search in Google Scholar

[29] M. Mackaay, M. Stošić and P. Vaz, A diagrammatic categorification of the q-Schur algebra, Quantum Topol. 4 (2013), no. 1, 1–75. 10.4171/QT/34Search in Google Scholar

[30] A. Mellit, Homology of torus knots, preprint (2017), http://arxiv.org/abs/1704.07630. 10.2140/gt.2022.26.47Search in Google Scholar

[31] A. Oblomkov and L. Rozansky, HOMFLYPT homology of Coxeter links, preprint (2017), http://arxiv.org/abs/arXiv:1706.00124. Search in Google Scholar

[32] A. Oblomkov and L. Rozansky, Knot homology and sheaves on the Hilbert scheme of points on the plane, Selecta Math. (N. S.) 24 (2018), no. 3, 2351–2454. 10.1007/s00029-017-0385-8Search in Google Scholar

[33] A. Oblomkov and L. Rozansky, Affine braid group, JM elements and knot homology, Transform. Groups 24 (2019), no. 2, 531–544. 10.1007/s00031-018-9478-5Search in Google Scholar

[34] J. Rasmussen, Khovanov homology and the slice genus, Invent. Math. 182 (2010), no. 2, 419–447. 10.1007/s00222-010-0275-6Search in Google Scholar

[35] D. E. V. Rose and P. Wedrich, Deformations of colored 𝔰⁢𝔩N link homologies via foams, Geom. Topol. 20 (2016), no. 6, 3431–3517. 10.2140/gt.2016.20.3431Search in Google Scholar

[36] M. Stošić, Indecomposable objects and Lusztig’s canonical basis, Math. Res. Lett. 22 (2015), no. 1, 245–278. 10.4310/MRL.2015.v22.n1.a13Search in Google Scholar

[37] M. Stošić, On extended graphical calculus for categorified quantum s⁢l⁢(n), preprint (2016), http://arxiv.org/abs/1605.06810. Search in Google Scholar

[38] M. Varagnolo and E. Vasserot, Canonical bases and KLR-algebras, J. reine angew. Math. 659 (2011), 67–100. 10.1515/crelle.2011.068Search in Google Scholar

[39] B. Webster, Unfurling Khovanov–Lauda–Rouquier algebras, preprint (2016), https://arxiv.org/abs/1603.06311. Search in Google Scholar

[40] H. Wu, Equivariant colored 𝔰⁢𝔩⁢(N)-homology for links, J. Knot Theory Ramifications 21 (2012), no. 2, Article ID 1250012. 10.1142/S0218216511009558Search in Google Scholar