Lattice cohomology and q-series invariants of 3-manifolds

References

[1] K. Bringmann, K. Mahlburg and A. Milas, Quantum modular forms and plumbing graphs of 3-manifolds, J. Combin. Theory Ser. A 170 (2020), Article ID 105145. 10.1016/j.jcta.2019.105145Search in Google Scholar

[2] M. C. Cheng, S. Chun, F. Ferrari, S. Gukov and S. M. Harrison, 3d modularity, J. High Energy Phys. 2019 (2019), Article ID 10. 10.1007/JHEP10(2019)010Search in Google Scholar

[3] I. Dai and C. Manolescu, Involutive Heegaard Floer homology and plumbed three-manifolds, J. Inst. Math. Jussieu 18 (2019), no. 6, 1115–1155. 10.1017/S1474748017000329Search in Google Scholar

[4] S. K. Donaldson, An application of gauge theory to four-dimensional topology, J. Differential Geom. 18 (1983), no. 2, 279–315. 10.4310/jdg/1214437665Search in Google Scholar

[5] A. Floer, An instanton-invariant for 3-manifolds, Comm. Math. Phys. 118 (1988), no. 2, 215–240. 10.1007/BF01218578Search in Google Scholar

[6] R. E. Gompf and A. I. Stipsicz, 4-manifolds and Kirby calculus, Grad. Stud. Math. 20, American Mathematical Society, Providence 1999. 10.1090/gsm/020Search in Google Scholar

[7] S. Gukov and C. Manolescu, A two-variable series for knot complements, Quantum Topol. 12 (2021), no. 1, 1–109. 10.4171/QT/145Search in Google Scholar

[8] S. Gukov, S. Park and P. Putrov, Cobordism invariants from BPS q-series, Ann. Henri Poincaré 22 (2021), no. 12, 4173–4203. 10.1007/s00023-021-01089-2Search in Google Scholar

[9] S. Gukov, D. Pei, P. Putrov and C. Vafa, BPS spectra and 3-manifold invariants, J. Knot Theory Ramifications 29 (2020), no. 2, Article ID 2040003. 10.1142/S0218216520400039Search in Google Scholar

[10] S. Gukov, P. Putrov and C. Vafa, Fivebranes and 3-manifold homology, J. High Energy Phys. 2017 (2017), no. 7, Article ID 71. 10.1007/JHEP07(2017)071Search in Google Scholar

[11] K. Hendricks and C. Manolescu, Involutive Heegaard Floer homology, Duke Math. J. 166 (2017), no. 7, 1211–1299. 10.1215/00127094-3793141Search in Google Scholar

[12] P. K. Johnson, Plum: A computer program for analyzing plumbed 3-manifolds, https://github.com/peterkj1/plum. Search in Google Scholar

[13] V. F. R. Jones, A polynomial invariant for knots via von Neumann algebras, Bull. Amer. Math. Soc. (N. S.) 12 (1985), no. 1, 103–111. 10.1090/S0273-0979-1985-15304-2Search in Google Scholar

[14] R. Lawrence and D. Zagier, Modular forms and quantum invariants of 3-manifolds, Asian J. Math. 3 (1999), 93–107. 10.4310/AJM.1999.v3.n1.a5Search in Google Scholar

[15] A. Némethi, On the Ozsváth–Szabó invariant of negative definite plumbed 3-manifolds, Geom. Topol. 9 (2005), 991–1042. 10.2140/gt.2005.9.991Search in Google Scholar

[16] A. Némethi, Lattice cohomology of normal surface singularities, Publ. Res. Inst. Math. Sci. 44 (2008), no. 2, 507–543. 10.2977/prims/1210167336Search in Google Scholar

[17] W. D. Neumann, A calculus for plumbing applied to the topology of complex surface singularities and degenerating complex curves, Trans. Amer. Math. Soc. 268 (1981), no. 2, 299–344. 10.1090/S0002-9947-1981-0632532-8Search in Google Scholar

[18] P. Ozsváth, A. I. Stipsicz and Z. Szabó, A spectral sequence on lattice homology, Quantum Topol. 5 (2014), no. 4, 487–521. 10.4171/QT/56Search in Google Scholar

[19] P. Ozsváth, A. I. Stipsicz and Z. Szabó, Knots in lattice homology, Comment. Math. Helv. 89 (2014), no. 4, 783–818. 10.4171/CMH/334Search in Google Scholar

[20] P. Ozsváth and Z. Szabó, On the Floer homology of plumbed three-manifolds, Geom. Topol. 7 (2003), 185–224. 10.2140/gt.2003.7.185Search in Google Scholar

[21] P. Ozsváth and Z. Szabó, Holomorphic disks and three-manifold invariants: Properties and applications, Ann. of Math. (2) 159 (2004), no. 3, 1159–1245. 10.4007/annals.2004.159.1159Search in Google Scholar

[22] P. Ozsváth and Z. Szabó, Holomorphic disks and topological invariants for closed three-manifolds, Ann. of Math. (2) 159 (2004), no. 3, 1027–1158. 10.4007/annals.2004.159.1027Search in Google Scholar

[23] N. Reshetikhin and V. G. Turaev, Invariants of 3-manifolds via link polynomials and quantum groups, Invent. Math. 103 (1991), no. 3, 547–597. 10.1007/BF01239527Search in Google Scholar

[24] E. Witten, Quantum field theory and the Jones polynomial, Comm. Math. Phys. 121 (1989), no. 3, 351–399. 10.1007/BF01217730Search in Google Scholar

[25] D. Zagier, Quantum modular forms, Quanta of maths, Clay Math. Proc. 11, American Mathematical Society, Providence (2010), 659–675. Search in Google Scholar

[26] I. Zemke, Bordered manifolds with torus boundary and the link surgery formula, preprint (2022), https://arxiv.org/abs/2109.11520v4. Search in Google Scholar

[27] I. Zemke, The equivalence of lattice and Heegaard Floer homology, preprint (2022), https://arxiv.org/abs/2111.14962. Search in Google Scholar