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Homological stability for moduli spaces of disconnected submanifolds, I

Martin Palmer

Algebraic & Geometric Topology 21 (2021) 1371–1444
Bibliography
1 N A Baas, On bordism theory of manifolds with singularities, Math. Scand. 33 (1973) 279 MR346824
2 T Banakh, K Mine, K Sakai, T Yagasaki, Homeomorphism and diffeomorphism groups of non-compact manifolds with the Whitney topology, Topology Proc. 37 (2011) 61 MR2643696
3 P Belmans, A J de Jong, others, The Stacks project, electronic reference (2005–)
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 S K Boldsen, Improved homological stability for the mapping class group with integral or twisted coefficients, Math. Z. 270 (2012) 297 MR2875835
7 T E Brendle, A Hatcher, Configuration spaces of rings and wickets, Comment. Math. Helv. 88 (2013) 131 MR3008915
8 F Cantero Morán, O Randal-Williams, Homological stability for spaces of embedded surfaces, Geom. Topol. 21 (2017) 1387 MR3650077
9 J Cerf, Topologie de certains espaces de plongements, Bull. Soc. Math. France 89 (1961) 227 MR140120
10 T Church, Homological stability for configuration spaces of manifolds, Invent. Math. 188 (2012) 465 MR2909770
11 T Church, B Farb, Representation theory and homological stability, Adv. Math. 245 (2013) 250 MR3084430
12 G Collinet, A Djament, J T Griffin, Stabilité homologique pour les groupes d’automorphismes des produits libres, Int. Math. Res. Not. 2013 (2013) 4451 MR3116169
13 A Dold, Decomposition theorems for S(n)–complexes, Ann. of Math. 75 (1962) 8 MR137113
14 A Dold, R Thom, Quasifaserungen und unendliche symmetrische Produkte, Ann. of Math. 67 (1958) 239 MR97062
15 J Ebert, O Randal-Williams, Semisimplicial spaces, Algebr. Geom. Topol. 19 (2019) 2099 MR3995026
16 S Galatius, O Randal-Williams, Stable moduli spaces of high-dimensional manifolds, Acta Math. 212 (2014) 257 MR3207759
17 S Galatius, O Randal-Williams, Homological stability for moduli spaces of high dimensional manifolds, I, J. Amer. Math. Soc. 31 (2018) 215 MR3718454
18 M Golubitsky, V Guillemin, Stable mappings and their singularities, 14, Springer (1973) MR0341518
19 J T Griffin, Diagonal complexes and the integral homology of the automorphism group of a free product, Proc. Lond. Math. Soc. 106 (2013) 1087 MR3066749
20 I I Guran, M M Zarichnyi, The Whitney topology and box products, Dokl. Akad. Nauk Ukrain. SSR Ser. A 1984 (1984) 5 MR775570
21 S Haller, Groups of diffeomorphisms, Master’s thesis, University of Vienna (1995)
22 J L Harer, Stability of the homology of the mapping class groups of orientable surfaces, Ann. of Math. 121 (1985) 215 MR786348
23 A Hatcher, N Wahl, Stabilization for mapping class groups of 3–manifolds, Duke Math. J. 155 (2010) 205 MR2736166
24 M W Hirsch, Differential topology, 33, Springer (1976) MR0448362
25 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
26 A Kriegl, P W Michor, The convenient setting of global analysis, 53, Amer. Math. Soc. (1997) MR1471480
27 A Kupers, Homological stability for unlinked circles in a 3–manifold, Q. J. Math. 71 (2020) 335 MR4077198
28 A Kupers, J Miller, Homological stability for topological chiral homology of completions, Adv. Math. 292 (2016) 755 MR3464033
29 E L Lima, On the local triviality of the restriction map for embeddings, Comment. Math. Helv. 38 (1964) 163 MR161343
30 J N Mather, Stability of C mappings, II : Infinitesimal stability implies stability, Ann. of Math. 89 (1969) 254 MR259953
31 J McCleary, A user’s guide to spectral sequences, 58, Cambridge Univ. Press (2001) MR1793722
32 D McDuff, Configuration spaces of positive and negative particles, Topology 14 (1975) 91 MR358766
33 P W Michor, Manifolds of differentiable mappings, 3, Shiva (1980) MR583436
34 P Michor, Manifolds of smooth maps, III : The principal bundle of embeddings of a noncompact smooth manifold, Cahiers Topol. Géom. Diff. 21 (1980) 325 MR591389
35 R S Palais, Local triviality of the restriction map for embeddings, Comment. Math. Helv. 34 (1960) 305 MR123338
36 M Palmer, Homological stability for oriented configuration spaces, Trans. Amer. Math. Soc. 365 (2013) 3675 MR3042599
37 M Palmer, Twisted homological stability for configuration spaces, Homology Homotopy Appl. 20 (2018) 145 MR3806572
38 M Palmer, Stability for moduli spaces of manifolds with conical singularities, preprint (2020) arXiv:1807.07558
39 N Perlmutter, Linking forms and stabilization of diffeomorphism groups of manifolds of dimension 4n + 1, J. Topol. 9 (2016) 552 MR3509973
40 O Randal-Williams, Homological stability for unordered configuration spaces, Q. J. Math. 64 (2013) 303 MR3032101
41 O Randal-Williams, Resolutions of moduli spaces and homological stability, J. Eur. Math. Soc. 18 (2016) 1 MR3438379
42 G Segal, Configuration-spaces and iterated loop-spaces, Invent. Math. 21 (1973) 213 MR331377
43 G Segal, The topology of spaces of rational functions, Acta Math. 143 (1979) 39 MR533892
44 J Strom, Modern classical homotopy theory, 127, Amer. Math. Soc. (2011) MR2839990
45 D Sullivan, On the Hauptvermutung for manifolds, Bull. Amer. Math. Soc. 73 (1967) 598 MR212811
46 R M Switzer, Algebraic topology: homotopy and homology, 212, Springer (1975) MR0385836
47 U Tillmann, Homology stability for symmetric diffeomorphism and mapping class groups, Math. Proc. Cambridge Philos. Soc. 160 (2016) 121 MR3432333
48 T Tran, Homological stability for subgroups of surface braid groups, preprint (2014) arXiv:1410.0923
49 N Wahl, Homological stability for mapping class groups of surfaces, from: "Handbook of moduli, III" (editors G Farkas, I Morrison), Adv. Lect. Math. 26, International (2013) 547 MR3135444
50 H Whitney, Differentiable manifolds, Ann. of Math. 37 (1936) 645 MR1503303
51 J C H Wilson, Representation stability for the cohomology of the pure string motion groups, Algebr. Geom. Topol. 12 (2012) 909 MR2928898