Geometry & Topology Volume 21, issue 5 (2017)

Download this article
	For screen
	For printing

Recent Issues

The Journal

Submission Guidelines

Submission Page

Policies for Authors

Ethics Statement

ISSN 1364-0380 (online)

ISSN 1465-3060 (print)

Author Index

To Appear

Other MSP Journals

Stable homology of surface diffeomorphism groups made discrete

Sam Nariman

Geometry & Topology 21 (2017) 3047–3092

DOI: 10.2140/gt.2017.21.3047

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