Geometry & Topology Volume 23, issue 5 (2019)

Download this article
	For screen
	For printing

Recent Issues

The Journal

Submission Guidelines

Submission Page

Ethics Statement

ISSN (electronic): 1364-0380

ISSN (print): 1465-3060

Author Index

To Appear

Other MSP Journals

Homological stability of topological moduli spaces

Manuel Krannich

Geometry & Topology 23 (2019) 2397–2474

DOI: 10.2140/gt.2019.23.2397

Bibliography

1	V I Arnold, Braids of algebraic functions and cohomologies of swallowtails, Uspehi Mat. Nauk 23 (1968) 247 MR0231828
2	V I Arnold, The cohomology ring of the colored braid group, Mat. Zametki 5 (1969) 227 MR0242196
3	C Berger, I Moerdijk, Resolution of coloured operads and rectification of homotopy algebras, from: "Categories in algebra, geometry and mathematical physics" (editors A Davydov, M Batanin, M Johnson, S Lack, A Neeman), Contemp. Math. 431, Amer. Math. Soc. (2007) 31 MR2342815
4	S Betley, Twisted homology of symmetric groups, Proc. Amer. Math. Soc. 130 (2002) 3439 MR1918818
5	E Binz, H R Fischer, The manifold of embeddings of a closed manifold, from: "Differential geometric methods in mathematical physics" (editor H D Doebner), Lecture Notes in Phys. 139, Springer (1981) 310 MR613004
6	J M Boardman, R M Vogt, Homotopy invariant algebraic structures on topological spaces, 347, Springer (1973) MR0420609
7	C F Bödigheimer, F R Cohen, R J Milgram, Truncated symmetric products and configuration spaces, Math. Z. 214 (1993) 179 MR1240884
8	C F Bödigheimer, F Cohen, L Taylor, On the homology of configuration spaces, Topology 28 (1989) 111 MR991102
9	S K Boldsen, Improved homological stability for the mapping class group with integral or twisted coefficients, Math. Z. 270 (2012) 297 MR2875835
10	F Cantero, M Palmer, On homological stability for configuration spaces on closed background manifolds, Doc. Math. 188 (2015) 753 MR3398727
11	K Casto, FI_G–modules, orbit configuration spaces, and complex reflection groups, preprint (2016) arXiv:1608.06317
12	T Church, Homological stability for configuration spaces of manifolds, Invent. Math. 188 (2012) 465 MR2909770
13	T Church, J S Ellenberg, Homology of FI–modules, Geom. Topol. 21 (2017) 2373 MR3654111
14	T Church, J S Ellenberg, B Farb, FI–modules and stability for representations of symmetric groups, Duke Math. J. 164 (2015) 1833 MR3357185
15	T Church, J S Ellenberg, B Farb, R Nagpal, FI–modules over Noetherian rings, Geom. Topol. 18 (2014) 2951 MR3285226
16	T Church, B Farb, Representation theory and homological stability, Adv. Math. 245 (2013) 250 MR3084430
17	R L Cohen, I Madsen, Surfaces in a background space and the homology of mapping class groups, from: "Algebraic geometry, I: Seattle 2005" (editors D Abramovich, A Bertram, L Katzarkov, R Pandharipande, M Thaddeus), Proc. Sympos. Pure Math. 80, Amer. Math. Soc. (2009) 43 MR2483932
18	D Crowley, J Sixt, Stably diffeomorphic manifolds and l_2q+1(ℤ[π]), Forum Math. 23 (2011) 483 MR2805192
19	R De Sapio, On (k−1)–connected (2k+1)–manifolds, Math. Scand. 25 (1970) 181 MR0261614
20	W G Dwyer, Twisted homological stability for general linear groups, Ann. of Math. 111 (1980) 239 MR569072
21	C J Earle, J Eells, The diffeomorphism group of a compact Riemann surface, Bull. Amer. Math. Soc. 73 (1967) 557 MR212840
22	J Ebert, O Randal-Williams, Semisimplicial spaces, Algebr. Geom. Topol. 19 (2019) 2099
23	Z Fiedorowicz, M Stelzer, R M Vogt, Homotopy colimits of algebras over 𝒞at–operads and iterated loop spaces, Adv. Math. 248 (2013) 1089 MR3107537
24	B Fresse, Homotopy of operads and Grothendieck–Teichmüller groups, I : The algebraic theory and its topological background, 217, Amer. Math. Soc. (2017) MR3643404
25	N Friedrich, Homological stability of automorphism groups of quadratic modules and manifolds, Doc. Math. 22 (2017) 1729 MR3760514
26	W Fulton, J Harris, Representation theory, 129, Springer (1991) MR1153249
27	S Galatius, O Randal-Williams, Homological stability for moduli spaces of high dimensional manifolds, II, Ann. of Math. 186 (2017) 127 MR3665002
28	S Galatius, O Randal-Williams, Homological stability for moduli spaces of high dimensional manifolds, I, J. Amer. Math. Soc. 31 (2018) 215 MR3718454
29	W L Gan, L Li, Coinduction functor in representation stability theory, J. Lond. Math. Soc. 92 (2015) 689 MR3431657
30	G Gandini, N Wahl, Homological stability for automorphism groups of RAAGs, Algebr. Geom. Topol. 16 (2016) 2421 MR3546470
31	A Gramain, Le type d’homotopie du groupe des difféomorphismes d’une surface compacte, Ann. Sci. École Norm. Sup. 6 (1973) 53 MR0326773
32	D Grayson, Higher algebraic K–theory, II (after Daniel Quillen), from: "Algebraic K–theory" (editors A Dold, B Eckmann), Lecture Notes in Math. 551, Springer (1976) 217 MR0574096
33	M A Guest, A Kozlowsky, K Yamaguchi, Homological stability of oriented configuration spaces, J. Math. Kyoto Univ. 36 (1996) 809 MR1443749
34	J L Harer, Stability of the homology of the mapping class groups of orientable surfaces, Ann. of Math. 121 (1985) 215 MR786348
35	A Hatcher, K Vogtmann, Tethers and homology stability for surfaces, Algebr. Geom. Topol. 17 (2017) 1871 MR3677942
36	A Hatcher, N Wahl, Stabilization for mapping class groups of 3–manifolds, Duke Math. J. 155 (2010) 205 MR2736166
37	R Hepworth, Homological stability for families of Coxeter groups, Algebr. Geom. Topol. 16 (2016) 2779 MR3572348
38	N V Ivanov, On the homology stability for Teichmüller modular groups : closed surfaces and twisted coefficients, from: "Mapping class groups and moduli spaces of Riemann surfaces" (editors C F Bödigheimer, R M Hain), Contemp. Math. 150, Amer. Math. Soc. (1993) 149 MR1234264
39	R Jimenez Rolland, Representation stability for the cohomology of the moduli space ℳ_gⁿ, Algebr. Geom. Topol. 11 (2011) 3011 MR2869450
40	R Jiménez Rolland, On the cohomology of pure mapping class groups as FI–modules, J. Homotopy Relat. Struct. 10 (2015) 401 MR3385692
41	W van der Kallen, Homology stability for linear groups, Invent. Math. 60 (1980) 269 MR586429
42	A Kupers, Proving homological stability for homeomorphisms of manifolds, preprint (2015) arXiv:1510.02456
43	A Kupers, J Miller, E_n–cell attachments and a local-to-global principle for homological stability, Math. Ann. 370 (2018) 209 MR3747486
44	J P May, The geometry of iterated loop spaces, 271, Springer (1972) MR0420610
45	J P May, J Sigurdsson, Parametrized homotopy theory, 132, Amer. Math. Soc. (2006) MR2271789
46	D McDuff, Configuration spaces of positive and negative particles, Topology 14 (1975) 91 MR0358766
47	J Miller, M Palmer, A twisted homology fibration criterion and the twisted group-completion theorem, Q. J. Math. 66 (2015) 265 MR3356291
48	J Miller, J C H Wilson, Higher-order representation stability and ordered configuration spaces of manifolds, Geom. Topol. 23 (2019) 2519
49	B Mirzaii, W van der Kallen, Homology stability for unitary groups, Doc. Math. 7 (2002) 143 MR1911214
50	R S Palais, Local triviality of the restriction map for embeddings, Comment. Math. Helv. 34 (1960) 305 MR0123338
51	M Palmer, Homological stability for oriented configuration spaces, Trans. Amer. Math. Soc. 365 (2013) 3675 MR3042599
52	M Palmer, Twisted homological stability for configuration spaces, Homology Homotopy Appl. 20 (2018) 145 MR3806572
53	P Patzt, X Wu, Stability results for Houghton groups, Algebr. Geom. Topol. 16 (2016) 2365 MR3546468
54	N Perlmutter, Homological stability for the moduli spaces of products of spheres, Trans. Amer. Math. Soc. 368 (2016) 5197 MR3456177
55	N Perlmutter, Linking forms and stabilization of diffeomorphism groups of manifolds of dimension 4n + 1, J. Topol. 9 (2016) 552 MR3509973
56	D Petersen, A spectral sequence for stratified spaces and configuration spaces of points, Geom. Topol. 21 (2017) 2527 MR3654116
57	E Ramos, On the degree-wise coherence of FI_G–modules, New York J. Math. 23 (2017) 873 MR3690235
58	O Randal-Williams, Homological stability for unordered configuration spaces, Q. J. Math. 64 (2013) 303 MR3032101
59	O Randal-Williams, Resolutions of moduli spaces and homological stability, J. Eur. Math. Soc. 18 (2016) 1 MR3438379
60	O Randal-Williams, Cohomology of automorphism groups of free groups with twisted coefficients, Selecta Math. 24 (2018) 1453 MR3782426
61	O Randal-Williams, N Wahl, Homological stability for automorphism groups, Adv. Math. 318 (2017) 534 MR3689750
62	E Riehl, Categorical homotopy theory, 24, Cambridge Univ. Press (2014) MR3221774
63	S V Sam, A Snowden, Representations of categories of G–maps, J. Reine Angew. Math. 750 (2019) 197 MR3943321
64	C Schlichtkrull, M Solberg, Braided injections and double loop spaces, Trans. Amer. Math. Soc. 368 (2016) 7305 MR3471092
65	G Segal, Configuration-spaces and iterated loop-spaces, Invent. Math. 21 (1973) 213 MR0331377
66	G Segal, Categories and cohomology theories, Topology 13 (1974) 293 MR0353298
67	G Segal, The topology of spaces of rational functions, Acta Math. 143 (1979) 39
68	A Soulié, The Long–Moody construction and polynomial functors, Ann. Inst. Fourier (Grenoble) (2019)
69	M Szymik, N Wahl, The homology of the Higman–Thompson groups, Invent. Math. 216 (2019) 445 MR3953508
70	U Tillmann, Homology stability for symmetric diffeomorphism and mapping class groups, Math. Proc. Cambridge Philos. Soc. 160 (2016) 121 MR3432333
71	P Tosteson, Lattice spectral sequences and cohomology of configuration spaces, preprint (2016) arXiv:1612.06034
72	B Totaro, Configuration spaces of algebraic varieties, Topology 35 (1996) 1057 MR1404924
73	A A Voronov, The Swiss-cheese operad, from: "Homotopy invariant algebraic structures" (editors J P Meyer, J Morava, W S Wilson), Contemp. Math. 239, Amer. Math. Soc. (1999) 365 MR1718089
74	N Wahl, Homological stability for the mapping class groups of non-orientable surfaces, Invent. Math. 171 (2008) 389 MR2367024
75	C T C Wall, Classification problems in differential topology, VI : Classification of (s−1)–connected (2s+1)–manifolds, Topology 6 (1967) 273 MR0216510
76	G W Whitehead, Elements of homotopy theory, 61, Springer (1978) MR516508