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Quotient singularities, eta invariants, and self-dual metrics

Michael T Lock and Jeff A Viaclovsky

Geometry & Topology 20 (2016) 1773–1806
Bibliography
1 A G Ache, J A Viaclovsky, Asymptotics of the self-dual deformation complex, J. Geom. Anal. 25 (2015) 951 MR3319957
2 T M Apostol, Modular functions and Dirichlet series in number theory, 41, Springer (1990) MR1027834
3 T Ashikaga, M Ishizaka, Another form of the reciprocity law of Dedekind sum, (2008)
4 S Bando, A Kasue, H Nakajima, On a construction of coordinates at infinity on manifolds with fast curvature decay and maximal volume growth, Invent. Math. 97 (1989) 313 MR1001844
5 D Baraglia, Topological T-duality for general circle bundles, Pure Appl. Math. Q. 10 (2014) 367 MR3282986
6 E Brieskorn, Rationale Singularitäten komplexer Flächen, Invent. Math. 4 (1967/1968) 336 MR0222084
7 R L Bryant, Bochner–Kähler metrics, J. Amer. Math. Soc. 14 (2001) 623 MR1824987
8 D M J Calderbank, M A Singer, Einstein metrics and complex singularities, Invent. Math. 156 (2004) 405 MR2052611
9 X Chen, C LeBrun, B Weber, On conformally Kähler, Einstein manifolds, J. Amer. Math. Soc. 21 (2008) 1137 MR2425183
10 H S M Coxeter, The binary polyhedral groups, and other generalizations of the quaternion group, Duke Math. J. 7 (1940) 367 MR0003409
11 H S M Coxeter, Regular complex polytopes, Cambridge Univ. Press (1991) MR1119304
12 M G Dabkowski, M T Lock, On Kähler conformal compactifications of U(n)– invariant ALE spaces, Ann. Global Anal. Geom. 49 (2016) 73 MR3454025
13 L David, P Gauduchon, The Bochner-flat geometry of weighted projective spaces, from: "Perspectives in Riemannian geometry" (editors V Apostolov, A Dancer, N Hitchin, M Wang), CRM Proc. Lecture Notes 40, Amer. Math. Soc. (2006) 109 MR2237108
14 S Donaldson, R Friedman, Connected sums of self-dual manifolds and deformations of singular spaces, Nonlinearity 2 (1989) 197 MR994091
15 P Du Val, Homographies, quaternions and rotations, Clarendon Press (1964) MR0169108
16 T Eguchi, A J Hanson, Self-dual solutions to Euclidean gravity, Ann. Physics 120 (1979) 82 MR540896
17 A Floer, Self-dual conformal structures on lCP2, J. Differential Geom. 33 (1991) 551 MR1094469
18 D S Freed, K K Uhlenbeck, Instantons and four-manifolds, 1, Springer (1991) MR1081321
19 G W Gibbons, S W Hawking, Gravitational multi-instantons, Physics Letters B 78 (1978) 430
20 F Hirzebruch, Über vierdimensionale Riemannsche Flächenmehrdeutiger analytischer Funktionen von zwei komplexen Veränderlichen, Math. Ann. 126 (1953) 1 MR0062842
21 N J Hitchin, Einstein metrics and the eta-invariant, Boll. Un. Mat. Ital. B 11 (1997) 95 MR1456253
22 N Honda, Self-dual metrics and twenty-eight bitangents, J. Differential Geom. 75 (2007) 175 MR2286821
23 N Honda, Deformation of LeBrun’s ALE metrics with negative mass, Comm. Math. Phys. 322 (2013) 127 MR3073160
24 D Joyce, The hypercomplex quotient and the quaternionic quotient, Math. Ann. 290 (1991) 323 MR1109637
25 D D Joyce, Explicit construction of self-dual 4–manifolds, Duke Math. J. 77 (1995) 519 MR1324633
26 T Kawasaki, The index of elliptic operators over V –manifolds, Nagoya Math. J. 84 (1981) 135 MR641150
27 A Kovalev, M Singer, Gluing theorems for complete anti-self-dual spaces, Geom. Funct. Anal. 11 (2001) 1229 MR1878320
28 P B Kronheimer, The construction of ALE spaces as hyper-Kähler quotients, J. Differential Geom. 29 (1989) 665 MR992334
29 P B Kronheimer, A Torelli-type theorem for gravitational instantons, J. Differential Geom. 29 (1989) 685 MR992335
30 C LeBrun, Counter-examples to the generalized positive action conjecture, Comm. Math. Phys. 118 (1988) 591 MR962489
31 C LeBrun, Explicit self-dual metrics on CP2##CP2, J. Differential Geom. 34 (1991) 223 MR1114461
32 C LeBrun, B Maskit, On optimal 4–dimensional metrics, J. Geom. Anal. 18 (2008) 537 MR2393270
33 C LeBrun, M Singer, A Kummer-type construction of self-dual 4–manifolds, Math. Ann. 300 (1994) 165 MR1289837
34 M T Lock, J A Viaclovsky, Anti-self-dual orbifolds with cyclic quotient singularities, J. Eur. Math. Soc. (JEMS) 17 (2015) 2805 MR3420523
35 M T Lock, J A Viaclovsky, A smörgåsbord of scalar-flat Kähler ALE surfaces, J. Reine Angew. Math. (2016)
36 D McCullough, Isometries of elliptic 3–manifolds, J. London Math. Soc. 65 (2002) 167 MR1875143
37 H Nakajima, Self-duality of ALE Ricci-flat 4–manifolds and positive mass theorem, from: "Recent topics in differential and analytic geometry" (editor T Ochiai), Adv. Stud. Pure Math. 18, Academic Press (1990) 385 MR1145266
38 P Scott, The geometries of 3–manifolds, Bull. London Math. Soc. 15 (1983) 401 MR705527
39 R Stekolshchik, Notes on Coxeter transformations and the McKay correspondence, Springer (2008) MR2388772
40 I Şuvaina, ALE Ricci-flat Kähler metrics and deformations of quotient surface singularities, Ann. Global Anal. Geom. 41 (2012) 109 MR2860399
41 G Tian, J Viaclovsky, Moduli spaces of critical Riemannian metrics in dimension four, Adv. Math. 196 (2005) 346 MR2166311
42 J A Viaclovsky, An index theorem on anti-self-dual orbifolds, Int. Math. Res. Not. 2013 (2013) 3911 MR3096914
43 E P Wright, Quotients of gravitational instantons, Ann. Global Anal. Geom. 41 (2012) 91 MR2860398