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On Ruan's cohomological crepant resolution conjecture for the complexified Bianchi orbifolds

Fabio Perroni and Alexander D Rahm

Algebraic & Geometric Topology 19 (2019) 2715–2762
Bibliography
1 A Adem, J Leida, Y Ruan, Orbifolds and stringy topology, 171, Cambridge Univ. Press (2007) MR2359514
2 R Aurich, F Steiner, H Then, Numerical computation of Maass waveforms and an application to cosmology, from: "Hyperbolic geometry and applications in quantum chaos and cosmology" (editors J Bolte, F Steiner), London Math. Soc. Lecture Note Ser. 397, Cambridge Univ. Press (2012) 229 MR2895235
3 W L Baily Jr., A Borel, Compactification of arithmetic quotients of bounded symmetric domains, Ann. of Math. 84 (1966) 442 MR0216035
4 E Berkove, A D Rahm, The mod 2 cohomology rings of SL2 of the imaginary quadratic integers, J. Pure Appl. Algebra 220 (2016) 944 MR3414403
5 L Bianchi, Sui gruppi di sostituzioni lineari con coefficienti appartenenti a corpi quadratici immaginarî, Math. Ann. 40 (1892) 332 MR1510727
6 S Boissière, E Mann, F Perroni, The cohomological crepant resolution conjecture for (1,3,4,4), Internat. J. Math. 20 (2009) 791 MR2541935
7 T Bridgeland, A King, M Reid, The McKay correspondence as an equivalence of derived categories, J. Amer. Math. Soc. 14 (2001) 535 MR1824990
8 E Brieskorn, Über die Auflösung gewisser Singularitäten von holomorphen Abbildungen, Math. Ann. 166 (1966) 76 MR0206973
9 J C Chen, H H Tseng, A note on derived McKay correspondence, Math. Res. Lett. 15 (2008) 435 MR2407221
10 W Chen, Y Ruan, Orbifold Gromov–Witten theory, from: "Orbifolds in mathematics and physics" (editors A Adem, J Morava, Y Ruan), Contemp. Math. 310, Amer. Math. Soc. (2002) 25 MR1950941
11 W Chen, Y Ruan, A new cohomology theory of orbifold, Comm. Math. Phys. 248 (2004) 1 MR2104605
12 T Coates, Y Ruan, Quantum cohomology and crepant resolutions: a conjecture, Ann. Inst. Fourier (Grenoble) 63 (2013) 431 MR3112518
13 J Elstrodt, F Grunewald, J Mennicke, Groups acting on hyperbolic space: harmonic analysis and number theory, Springer (1998) MR1483315
14 B Fantechi, L Göttsche, Orbifold cohomology for global quotients, Duke Math. J. 117 (2003) 197 MR1971293
15 B Fine, Algebraic theory of the Bianchi groups, 129, Dekker (1989) MR1010229
16 D Flöge, Zur Struktur der PSL2 über einigen imaginär-quadratischen Zahlringen, Math. Z. 183 (1983) 255 MR704107
17 O Forster, Lectures on Riemann surfaces, 81, Springer (1981) MR648106
18 W Fulton, Intersection theory, 2, Springer (1998) MR1644323
19 W M Goldman, Complex hyperbolic geometry, Clarendon (1999) MR1695450
20 A González, E Lupercio, C Segovia, B Uribe, Orbifold topological quantum field theories in dimension 2, book project (2013)
21 A Hatcher, Algebraic topology, Cambridge Univ. Press (2002) MR1867354
22 Y Ito, M Reid, The McKay correspondence for finite subgroups of SL(3, ), from: "Higher-dimensional complex varieties" (editors M Andreatta, T Peternell), de Gruyter (1996) 221 MR1463181
23 F Klein, Ueber binäre Formen mit linearen Transformationen in sich selbst, Math. Ann. 9 (1875) 183 MR1509857
24 N Krämer, Die Konjugationsklassenzahlen der endlichen Untergruppen in der Norm-Eins-Gruppe von Maximalordnungen in Quaternionenalgebren, Diplomarbeit, Universität Bonn (1980)
25 N Krämer, Beiträge zur Arithmetik imaginärquadratischer Zahlkörper, PhD thesis, Universität Bonn (1984) MR806543
26 C Maclachlan, A W Reid, The arithmetic of hyperbolic 3–manifolds, 219, Springer (2003) MR1937957
27 W S Massey, A basic course in algebraic topology, 127, Springer (1991) MR1095046
28 G Mislin, A Valette, Proper group actions and the Baum–Connes conjecture, Birkhäuser (2003) MR2027168
29 J Morrow, K Kodaira, Complex manifolds, Holt, Rinehart and Winston (1971) MR2214741
30 F Perroni, Chen–Ruan cohomology of ADE singularities, Internat. J. Math. 18 (2007) 1009 MR2360646
31 H Poincaré, Mémoire : les groupes kleinéens, Acta Math. 3 (1883) 49 MR1554613
32 A Rahm, Bianchi.gp, software (2010)
33 A Rahm, (Co)homologies and K–theory of Bianchi groups using computational geometric models, PhD thesis, Institut Fourier, Université de Grenoble et Universität Göttingen (2010)
34 A D Rahm, On a question of Serre, C. R. Math. Acad. Sci. Paris 350 (2012) 741 MR2981344
35 A D Rahm, Higher torsion in the abelianization of the full Bianchi groups, LMS J. Comput. Math. 16 (2013) 344 MR3109616
36 A D Rahm, The homological torsion of PSL2 of the imaginary quadratic integers, Trans. Amer. Math. Soc. 365 (2013) 1603 MR3003276
37 A D Rahm, Accessing the cohomology of discrete groups above their virtual cohomological dimension, J. Algebra 404 (2014) 152 MR3177890
38 A D Rahm, On the equivariant K–homology of PSL2 of the imaginary quadratic integers, Ann. Inst. Fourier (Grenoble) 66 (2016) 1667 MR3494182
39 A D Rahm, M Fuchs, The integral homology of PSL2 of imaginary quadratic integers with nontrivial class group, J. Pure Appl. Algebra 215 (2011) 1443 MR2769243
40 S S Roan, Minimal resolutions of Gorenstein orbifolds in dimension three, Topology 35 (1996) 489 MR1380512
41 Y Ruan, The cohomology ring of crepant resolutions of orbifolds, from: "Gromov–Witten theory of spin curves and orbifolds" (editors T J Jarvis, T Kimura, A Vaintrob), Contemp. Math. 403, Amer. Math. Soc. (2006) 117 MR2234886
42 A Scheutzow, Computing rational cohomology and Hecke eigenvalues for Bianchi groups, J. Number Theory 40 (1992) 317 MR1154042
43 J P Serre, Linear representations of finite groups, 42, Springer (1977) MR0450380
44 G N Tjurina, Resolution of singularities of flat deformations of double rational points, Funkcional. Anal. i Priložen. 4 (1970) 77 MR0267129
45 K Vogtmann, Rational homology of Bianchi groups, Math. Ann. 272 (1985) 399 MR799670
46 E Zaslow, Topological orbifold models and quantum cohomology rings, Comm. Math. Phys. 156 (1993) 301 MR1233848