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The extended Bogomolny equations and generalized Nahm pole boundary condition

Siqi He and Rafe Mazzeo

Geometry & Topology 23 (2019) 2475–2517
Bibliography
1 M Abouzaid, C Manolescu, A sheaf-theoretic model for SL(2,C) Floer homology, preprint (2017) arXiv:1708.00289
2 P Albin, É Leichtnam, R Mazzeo, P Piazza, The signature package on Witt spaces, Ann. Sci. Éc. Norm. Supér. 45 (2012) 241 MR2977620
3 P Albin, E Leichtnam, R Mazzeo, P Piazza, Hodge theory on Cheeger spaces, J. Reine Angew. Math. 744 (2018) 29 MR3871440
4 M F Atiyah, Geometry of Yang–Mills fields, from: "Mathematical problems in theoretical physics" (editors G Dell’Antonio, S Doplicher, G Jona-Lasinio), Lecture Notes in Phys. 80, Springer (1978) 216 MR518436
5 M Atiyah, New invariants of 3– and 4–dimensional manifolds, from: "The mathematical heritage of Hermann Weyl" (editor R O Wells Jr.), Proc. Sympos. Pure Math. 48, Amer. Math. Soc. (1988) 285 MR974342
6 L A Caffarelli, X Cabré, Fully nonlinear elliptic equations, 43, Amer. Math. Soc. (1995) MR1351007
7 P T Chruściel, R Mazzeo, Initial data sets with ends of cylindrical type, I : The Lichnerowicz equation, Ann. Henri Poincaré 16 (2015) 1231 MR3324104
8 B Collier, Q Li, Asymptotics of Higgs bundles in the Hitchin component, Adv. Math. 307 (2017) 488 MR3590524
9 A Daemi, K Fukaya, Atiyah–Floer conjecture : a formulation, a strategy of proof and generalizations, from: "Modern geometry : a celebration of the work of Simon Donaldson" (editors V Muñoz, I Smith, R P Thomas), Proc. Sympos. Pure Math. 99, Amer. Math. Soc. (2018) 23 MR3838878
10 S K Donaldson, Anti self-dual Yang–Mills connections over complex algebraic surfaces and stable vector bundles, Proc. London Math. Soc. 50 (1985) 1 MR765366
11 D Gaiotto, E Witten, Knot invariants from four-dimensional gauge theory, Adv. Theor. Math. Phys. 16 (2012) 935 MR3024278
12 A Haydys, Fukaya–Seidel category and gauge theory, J. Symplectic Geom. 13 (2015) 151 MR3338833
13 S He, A gluing theorem for the Kapustin–Witten equations with a Nahm pole, preprint (2017) arXiv:1707.06182
14 S He, The expansions of the Nahm pole solutions to the Kapustin–Witten equations, preprint (2018) arXiv:1808.03886
15 N J Hitchin, The self-duality equations on a Riemann surface, Proc. London Math. Soc. 55 (1987) 59 MR887284
16 N J Hitchin, Lie groups and Teichmüller space, Topology 31 (1992) 449 MR1174252
17 H Ishii, P L Lions, Viscosity solutions of fully nonlinear second-order elliptic partial differential equations, J. Differential Equations 83 (1990) 26 MR1031377
18 A Kapustin, E Witten, Electric-magnetic duality and the geometric Langlands program, Commun. Number Theory Phys. 1 (2007) 1 MR2306566
19 P B Kronheimer, Instantons and the geometry of the nilpotent variety, J. Differential Geom. 32 (1990) 473 MR1072915
20 R Mazzeo, Elliptic theory of differential edge operators, I, Comm. Partial Differential Equations 16 (1991) 1615 MR1133743
21 R Mazzeo, E Witten, The Nahm pole boundary condition, from: "The influence of Solomon Lefschetz in geometry and topology" (editors L Katzarkov, E Lupercio, F J Turrubiates), Contemp. Math. 621, Amer. Math. Soc. (2014) 171 MR3289327
22 R Mazzeo, E Witten, The KW equations and the Nahm pole boundary condition with knots, preprint (2017) arXiv:1712.00835
23 J Milnor, On the existence of a connection with curvature zero, Comment. Math. Helv. 32 (1958) 215 MR95518
24 C H Taubes, Compactness theorems for SL(2;C) generalizations of the 4–dimensional anti-self dual equations, preprint (2013) arXiv:1307.6447
25 C H Taubes, PSL(2; ) connections on 3–manifolds with L2 bounds on curvature, Camb. J. Math. 1 (2013) 239 MR3272050
26 K Uhlenbeck, S T Yau, On the existence of Hermitian–Yang–Mills connections in stable vector bundles, Comm. Pure Appl. Math. 39 (1986) MR861491
27 E Witten, Fivebranes and knots, Quantum Topol. 3 (2012) 1 MR2852941
28 E Witten, Two lectures on the Jones polynomial and Khovanov homology, from: "Lectures on geometry" (editor N M J Woodhouse), Oxford Univ. Press (2017) 1 MR3676591
29 E Witten, Two lectures on gauge theory and Khovanov homology, from: "Modern geometry : a celebration of the work of Simon Donaldson" (editors V Muñoz, I Smith, R P Thomas), Proc. Sympos. Pure Math. 99, Amer. Math. Soc. (2018) 393 MR3838889
30 J W Wood, Bundles with totally disconnected structure group, Comment. Math. Helv. 46 (1971) 257 MR293655