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Sutured manifolds and polynomial invariants from higher rank bundles

Aliakbar Daemi and Yi Xie

Geometry & Topology 24 (2020) 49–178
Bibliography
1 M F Atiyah, R Bott, The Yang–Mills equations over Riemann surfaces, Philos. Trans. Roy. Soc. London Ser. A 308 (1983) 523 MR702806
2 M F Atiyah, V K Patodi, I M Singer, Spectral asymmetry and Riemannian geometry, II, Math. Proc. Cambridge Philos. Soc. 78 (1975) 405 MR397798
3 V Y Baranovskiĭ, The cohomology ring of the moduli space of stable bundles with odd determinant, Izv. Ross. Akad. Nauk Ser. Mat. 58 (1994) 204 MR1307064
4 H U Boden, Unitary representations of Brieskorn spheres, Duke Math. J. 75 (1994) 193 MR1284819
5 H U Boden, S Friedl, Metabelian SL(n, ) representations of knot groups, Pacific J. Math. 238 (2008) 7 MR2443505
6 H U Boden, C M Herald, P A Kirk, E P Klassen, Gauge theoretic invariants of Dehn surgeries on knots, Geom. Topol. 5 (2001) 143 MR1825661
7 A Borel, Topology of Lie groups and characteristic classes, Bull. Amer. Math. Soc. 61 (1955) 397 MR72426
8 P J Braam, S K Donaldson, Floer’s work on instanton homology, knots and surgery, from: "The Floer memorial volume" (editors H Hofer, C H Taubes, A Weinstein, E Zehnder), Progr. Math. 133, Birkhäuser (1995) 195 MR1362829
9 P J Braam, S K Donaldson, Fukaya–Floer homology and gluing formulae for polynomial invariants, from: "The Floer memorial volume" (editors H Hofer, C H Taubes, A Weinstein, E Zehnder), Progr. Math. 133, Birkhäuser (1995) 257 MR1362830
10 V Colin, P Ghiggini, K Honda, Embedded contact homology and open book decompositions, preprint (2010) arXiv:1008.2734
11 V Colin, P Ghiggini, K Honda, M Hutchings, Sutures and contact homology, I, Geom. Topol. 15 (2011) 1749 MR2851076
12 L H Culler, The blowup formula for higher rank Donaldson invariants, PhD thesis, Massachusetts Institute of Technology (2014) MR3279020
13 L Culler, A Daemi, Y Xie, Surgery, polygons and SU(N)–Floer Homology, preprint (2017) arXiv:1712.09910
14 U V Desale, S Ramanan, Poincaré polynomials of the variety of stable bundles, Math. Ann. 216 (1975) 233 MR379497
15 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
16 S K Donaldson, The orientation of Yang–Mills moduli spaces and 4–manifold topology, J. Differential Geom. 26 (1987) 397 MR910015
17 S K Donaldson, Polynomial invariants for smooth four-manifolds, Topology 29 (1990) 257 MR1066174
18 S K Donaldson, Floer homology and algebraic geometry, from: "Vector bundles in algebraic geometry" (editors N J Hitchin, P E Newstead, W M Oxbury), London Math. Soc. Lecture Note Ser. 208, Cambridge Univ. Press (1995) 119 MR1338415
19 S K Donaldson, Floer homology groups in Yang–Mills theory, 147, Cambridge Univ. Press (2002) MR1883043
20 S K Donaldson, P B Kronheimer, The geometry of four-manifolds, Clarendon (1990) MR1079726
21 S Dostoglou, D A Salamon, Self-dual instantons and holomorphic curves, Ann. of Math. 139 (1994) 581 MR1283871
22 J D Edelstein, M Gómez-Reino, M Mariño, Blowup formulae in Donaldson–Witten theory and integrable hierarchies, Adv. Theor. Math. Phys. 4 (2000) 503 MR1838718
23 P M N Feehan, T G Leness, Witten’s conjecture for many four-manifolds of simple type, J. Eur. Math. Soc. 17 (2015) 899 MR3349302
24 R Fintushel, R J Stern, Instanton homology of Seifert fibred homology three spheres, Proc. London Math. Soc. 61 (1990) 109 MR1051101
25 R Fintushel, R J Stern, Donaldson invariants of 4–manifolds with simple type, J. Differential Geom. 42 (1995) 577 MR1367403
26 R Fintushel, R J Stern, The blowup formula for Donaldson invariants, Ann. of Math. 143 (1996) 529 MR1394968
27 A Floer, An instanton-invariant for 3–manifolds, Comm. Math. Phys. 118 (1988) 215 MR956166
28 A Floer, Instanton homology and Dehn surgery, from: "The Floer memorial volume" (editors H Hofer, C H Taubes, A Weinstein, E Zehnder), Progr. Math. 133, Birkhäuser (1995) 77 MR1362823
29 S Friedl, Eta invariants as sliceness obstructions and their relation to Casson–Gordon invariants, Algebr. Geom. Topol. 4 (2004) 893 MR2100685
30 R Friedman, Rank two vector bundles over regular elliptic surfaces, Invent. Math. 96 (1989) 283 MR989699
31 R Friedman, Vector bundles and SO(3)–invariants for elliptic surfaces, J. Amer. Math. Soc. 8 (1995) 29 MR1273414
32 R Friedman, J W Morgan, Smooth four-manifolds and complex surfaces, 27, Springer (1994) MR1288304
33 K Fukaya, Floer homology for oriented 3–manifolds, from: "Aspects of low-dimensional manifolds" (editors Y Matsumoto, S Morita), Adv. Stud. Pure Math. 20, Kinokuniya (1992) 1 MR1208307
34 D Gabai, Foliations and the topology of 3–manifolds, J. Differential Geom. 18 (1983) 445 MR723813
35 D Gabai, Foliations and the topology of 3–manifolds, Bull. Amer. Math. Soc. 8 (1983) 77 MR682826
36 D Gieseker, Geometric invariant theory and applications to moduli problems, from: "Invariant theory" (editor F Gherardelli), Lecture Notes in Math. 996, Springer (1983) 45 MR718126
37 D Gieseker, A construction of stable bundles on an algebraic surface, J. Differential Geom. 27 (1988) 137 MR918460
38 D Gieseker, J Li, Moduli of high rank vector bundles over surfaces, J. Amer. Math. Soc. 9 (1996) 107 MR1303031
39 R E Gompf, Nuclei of elliptic surfaces, Topology 30 (1991) 479 MR1113691
40 R E Gompf, A I Stipsicz, 4–manifolds and Kirby calculus, 20, Amer. Math. Soc. (1999) MR1707327
41 V Gritsenko, K Hulek, G K Sankaran, Abelianisation of orthogonal groups and the fundamental group of modular varieties, J. Algebra 322 (2009) 463 MR2529099
42 G Harder, M S Narasimhan, On the cohomology groups of moduli spaces of vector bundles on curves, Math. Ann. 212 (1974/75) 215 MR364254
43 R Hartshorne, Algebraic geometry, 52, Springer (1977) MR0463157
44 M Hutchings, Embedded contact homology and its applications, from: "Proceedings of the International Congress of Mathematicians, II" (editors R Bhatia, A Pal, G Rangarajan, V Srinivas, M Vanninathan, P Gastesi), Hindustan Book Agency (2010) 1022 MR2827830
45 M Hutchings, Lecture notes on embedded contact homology, from: "Contact and symplectic topology" (editors F Bourgeois, V Colin, A Stipsicz), Bolyai Soc. Math. Stud. 26, János Bolyai Math. Soc. (2014) 389 MR3220947
46 A Juhász, Holomorphic discs and sutured manifolds, Algebr. Geom. Topol. 6 (2006) 1429 MR2253454
47 A D King, P E Newstead, On the cohomology ring of the moduli space of rank 2 vector bundles on a curve, Topology 37 (1998) 407 MR1489212
48 R C Kirby editor, Problems in low-dimensional topology, from: "Geometric topology, II" (editor W H Kazez), AMS/IP Stud. Adv. Math. 2, Amer. Math. Soc. (1997) 35 MR1470751
49 K Kodaira, On compact complex analytic surfaces, I, Ann. of Math. 71 (1960) 111 MR132556
50 D Kotschick, SO(3)–invariants for 4–manifolds with b2+ = 1, Proc. London Math. Soc. 63 (1991) 426 MR1114516
51 D Kotschick, J W Morgan, SO(3)–invariants for 4–manifolds with b2+ = 1, II, J. Differential Geom. 39 (1994) 433 MR1267898
52 P B Kronheimer, Four-manifold invariants from higher-rank bundles, J. Differential Geom. 70 (2005) 59 MR2192061
53 P B Kronheimer, T S Mrowka, Recurrence relations and asymptotics for four-manifold invariants, Bull. Amer. Math. Soc. 30 (1994) 215 MR1246469
54 P B Kronheimer, T S Mrowka, Embedded surfaces and the structure of Donaldson’s polynomial invariants, J. Differential Geom. 41 (1995) 573 MR1338483
55 P Kronheimer, T Mrowka, Monopoles and three-manifolds, 10, Cambridge Univ. Press (2007) MR2388043
56 P Kronheimer, T Mrowka, Knots, sutures, and excision, J. Differential Geom. 84 (2010) 301 MR2652464
57 P B Kronheimer, T S Mrowka, Khovanov homology is an unknot-detector, Publ. Math. Inst. Hautes Études Sci. 113 (2011) 97 MR2805599
58 P B Kronheimer, T S Mrowka, Knot homology groups from instantons, J. Topol. 4 (2011) 835 MR2860345
59 P B Kronheimer, T S Mrowka, Tait colorings, and an instanton homology for webs and foams, J. Eur. Math. Soc. 21 (2019) 55 MR3880205
60 C Kutluhan, S Sivek, C H Taubes, Sutured ECH is a natural invariant, preprint (2013) arXiv:1312.3600
61 C LeBrun, Explicit self-dual metrics on P2 # # P2, J. Differential Geom. 34 (1991) 223 MR1114461
62 W P Li, Z Qin, Stable vector bundles on algebraic surfaces, Trans. Amer. Math. Soc. 345 (1994) 833 MR1260204
63 P Lisca, Computations of instanton invariants using Donaldson–Floer theory, Invent. Math. 119 (1995) 347 MR1312504
64 M Mariño, G Moore, The Donaldson–Witten function for gauge groups of rank larger than one, Comm. Math. Phys. 199 (1998) 25 MR1660219
65 D McDuff, D Salamon, J–holomorphic curves and symplectic topology, 52, Amer. Math. Soc. (2012) MR2954391
66 V B Mehta, A Ramanathan, Restriction of stable sheaves and representations of the fundamental group, Invent. Math. 77 (1984) 163 MR751136
67 J W Morgan, H Bass, editors, The Smith conjecture, 112, Academic (1984) MR758459
68 J W Morgan, T S Mrowka, A note on Donaldson’s polynomial invariants, Int. Math. Res. Not. 1992 (1992) 223 MR1191573
69 J W Morgan, T S Mrowka, The smooth classification of elliptic surfaces, from: "Geometry, topology, & physics" (editor S T Yau), Conf. Proc. Lecture Notes Geom. Topology 4, International (1995) 246 MR1358620
70 J W Morgan, T Mrowka, D Ruberman, The L2–moduli space and a vanishing theorem for Donaldson polynomial invariants, 2, International (1994) MR1287851
71 V Muñoz, Gluing formulae for Donaldson invariants for connected sums along surfaces, Asian J. Math. 1 (1997) 785 MR1621576
72 V Muñoz, Quantum cohomology of the moduli space of stable bundles over a Riemann surface, Duke Math. J. 98 (1999) 525 MR1695800
73 V Muñoz, Ring structure of the Floer cohomology of Σ × 𝕊1, Topology 38 (1999) 517 MR1670396
74 P Ozsváth, Z Szabó, Holomorphic disks and topological invariants for closed three-manifolds, Ann. of Math. 159 (2004) 1027 MR2113019
75 Y Ruan, G Tian, A mathematical theory of quantum cohomology, J. Differential Geom. 42 (1995) 259 MR1366548
76 D Ruberman, Relations among Donaldson invariants arising from negative 2–spheres and tori, Duke Math. J. 83 (1996) 645 MR1390659
77 D A Salamon, Quantum products for mapping tori and the Atiyah–Floer conjecture, from: "Northern California Symplectic Geometry Seminar" (editors Y Eliashberg, D Fuchs, T Ratiu, A Weinstein), Amer. Math. Soc. Transl. Ser. 2 196, Amer. Math. Soc. (1999) 199 MR1736219
78 B Siebert, G Tian, Recursive relations for the cohomology ring of moduli spaces of stable bundles, Turkish J. Math. 19 (1995) 131 MR1349566
79 C H Taubes, Self-dual connections on 4–manifolds with indefinite intersection matrix, J. Differential Geom. 19 (1984) 517 MR755237
80 C H Taubes, Casson’s invariant and gauge theory, J. Differential Geom. 31 (1990) 547 MR1037415
81 C H Taubes, L2 moduli spaces on 4–manifolds with cylindrical ends, 1, International (1993) MR1287854
82 W P Thurston, A norm for the homology of 3–manifolds, Mem. Amer. Math. Soc. 339, Amer. Math. Soc. (1986) 99 MR823443
83 W Wieczorek, The Donaldson invariant and embedded 2–spheres, J. Reine Angew. Math. 489 (1997) 15 MR1461204
84 E Witten, Monopoles and four-manifolds, Math. Res. Lett. 1 (1994) 769 MR1306021
85 Y Xie, On the framed singular instanton Floer homology from higher rank bundles, PhD thesis, Harvard University (2016) MR3706057
86 D Zagier, On the cohomology of moduli spaces of rank two vector bundles over curves, from: "The moduli space of curves" (editors R Dijkgraaf, C Faber, G van der Geer), Progr. Math. 129, Birkhäuser (1995) 533 MR1363070