#### Volume 21, issue 5 (2017)

 Download this article For screen For printing
 Recent Issues
 The Journal About the Journal Subscriptions Editorial Board Editorial Interests Editorial Procedure Submission Guidelines Submission Page Ethics Statement Author Index To Appear ISSN (electronic): 1364-0380 ISSN (print): 1465-3060 Other MSP Journals
Stable homology of surface diffeomorphism groups made discrete

### Sam Nariman

Geometry & Topology 21 (2017) 3047–3092
##### Bibliography
 1 T Akita, N Kawazumi, T Uemura, Periodic surface automorphisms and algebraic independence of Morita–Mumford classes, J. Pure Appl. Algebra 160 (2001) 1 MR1829309 2 R Bott, Lectures on characteristic classes and foliations, from: "Lectures on algebraic and differential topology" (editor S Gitler), Lecture Notes in Math. 279, Springer (1972) 1 MR0362335 3 J Bowden, The homology of surface diffeomorphism groups and a question of Morita, Proc. Amer. Math. Soc. 140 (2012) 2543 MR2898716 4 J Cheeger, J Simons, Differential characters and geometric invariants, from: "Geometry and topology" (editors J Alexander, J Harer), Lecture Notes in Math. 1167, Springer (1985) 50 MR827262 5 S Galatius, Mod p homology of the stable mapping class group, Topology 43 (2004) 1105 MR2079997 6 S Galatius, I Madsen, U Tillmann, Divisibility of the stable Miller–Morita–Mumford classes, J. Amer. Math. Soc. 19 (2006) 759 MR2219303 7 S Galatius, O Randal-Williams, Monoids of moduli spaces of manifolds, Geom. Topol. 14 (2010) 1243 MR2653727 8 S Galatius, O Randal-Williams, Stable moduli spaces of high-dimensional manifolds, Acta Math. 212 (2014) 257 MR3207759 9 S Galatius, U Tillmann, I Madsen, M Weiss, The homotopy type of the cobordism category, Acta Math. 202 (2009) 195 MR2506750 10 A Haefliger, Homotopy and integrability, from: "Manifolds" (editor N H Kuiper), Lecture Notes in Math. 197, Springer (1971) 133 MR0285027 11 J Harer, The second homology group of the mapping class group of an orientable surface, Invent. Math. 72 (1983) 221 MR700769 12 J L Harer, Stability of the homology of the mapping class groups of orientable surfaces, Ann. of Math. 121 (1985) 215 MR786348 13 J Harer, The third homology group of the moduli space of curves, Duke Math. J. 63 (1991) 25 MR1106936 14 S Hurder, Foliation geometry/topology problem set, preprint (2003) 15 U Koschorke, Singularities and bordism of q–plane fields and of foliations, Bull. Amer. Math. Soc. 80 (1974) 760 MR0358804 16 D Kotschick, S Morita, Signatures of foliated surface bundles and the symplectomorphism groups of surfaces, Topology 44 (2005) 131 MR2104005 17 D Kotschick, S Morita, Characteristic classes of foliated surface bundles with area-preserving holonomy, J. Differential Geom. 75 (2007) 273 MR2286823 18 H B Lawson Jr., The quantitative theory of foliations, 27, Amer. Math. Soc. (1977) MR0448368 19 I Madsen, U Tillmann, The stable mapping class group and Q(ℂP+∞), Invent. Math. 145 (2001) 509 MR1856399 20 I Madsen, M Weiss, The stable moduli space of Riemann surfaces : Mumford’s conjecture, Ann. of Math. 165 (2007) 843 MR2335797 21 J N Mather, Commutators of diffeomorphisms, Comment. Math. Helv. 49 (1974) 512 MR0356129 22 J Mather, On the homology of Haefliger’s classifying space, from: "Differential topology" (editor V Villani), CIME Summer Schools 73, Springer (2011) 71 23 J P May, K Ponto, More concise algebraic topology: localization, completion, and model categories, University of Chicago Press (2012) MR2884233 24 D McDuff, Local homology of groups of volume-preserving diffeomorphisms, III, Ann. Sci. École Norm. Sup. 16 (1983) 529 MR740589 25 J Milnor, The geometric realization of a semi-simplicial complex, Ann. of Math. 65 (1957) 357 MR0084138 26 J Milnor, Microbundles, I, Topology 3 (1964) 53 MR0161346 27 J Milnor, On the homology of Lie groups made discrete, Comment. Math. Helv. 58 (1983) 72 MR699007 28 T Mizutani, S Morita, T Tsuboi, On the cobordism classes of codimension one foliations which are almost without holonomy, Topology 22 (1983) 325 MR710106 29 S Morita, Discontinuous invariants of foliations, from: "Foliations" (editor I Tamura), Adv. Stud. Pure Math. 5, North-Holland (1985) 169 MR877332 30 S Morita, Characteristic classes of surface bundles, Invent. Math. 90 (1987) 551 MR914849 31 S Morita, Geometry of characteristic classes, 199, Amer. Math. Soc. (2001) MR1826571 32 S Morita, Cohomological structure of the mapping class group and beyond, from: "Problems on mapping class groups and related topics" (editor B Farb), Proc. Sympos. Pure Math. 74, Amer. Math. Soc. (2006) 329 MR2264550 33 S Nariman, Homological stability and stable moduli of flat manifold bundles, preprint (2014) arXiv:1406.6416 34 S Nariman, On the moduli space of flat symplectic surface bundles, preprint (2016) arXiv:1612.00043 35 H V Pittie, Characteristic classes of foliations, 10, Pitman (1976) MR0454988 36 J Powell, Two theorems on the mapping class group of a surface, Proc. Amer. Math. Soc. 68 (1978) 347 MR0494115 37 O Randal-Williams, Resolutions of moduli spaces and homological stability, J. Eur. Math. Soc. 18 (2016) 1 MR3438379 38 O H Rasmussen, Continuous variation of foliations in codimension two, Topology 19 (1980) 335 MR584559 39 Y B Rudyak, On Thom spectra, orientability, and cobordism, Springer (1998) MR1627486 40 F Sergeraert, BΓ [d’après John N Mather et William Thurston], from: "Séminaire Bourbaki (1977/78)", Lecture Notes in Math. 710, Springer (1979) 300 MR554229 41 S Smale, Diffeomorphisms of the 2–sphere, Proc. Amer. Math. Soc. 10 (1959) 621 MR0112149 42 P Teichner, Topological four-manifolds with finite fundamental group, Doktorarbeit, Johannes Gutenberg-Universität Mainz (1992) 43 W Thurston, Foliations and groups of diffeomorphisms, Bull. Amer. Math. Soc. 80 (1974) 304 MR0339267 44 U Tillmann, On the homotopy of the stable mapping class group, Invent. Math. 130 (1997) 257 MR1474157 45 T Tsuboi, On the foliated products of class C1, Ann. of Math. 130 (1989) 227 MR1014925 46 T Tsuboi, Classifying spaces for groupoid structures, from: "Foliations, geometry, and topology" (editors N C Saldanha, L Conlon, R Langevin, T Tsuboi, P Walczak), Contemp. Math. 498, Amer. Math. Soc. (2009) 67 MR2664590