Volume 23, issue 5 (2019)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 26
Issue 7, 2855–3306
Issue 6, 2405–2853
Issue 5, 1907–2404
Issue 4, 1435–1905
Issue 3, 937–1434
Issue 2, 477–936
Issue 1, 1–476

Volume 25, 7 issues

Volume 24, 7 issues

Volume 23, 7 issues

Volume 22, 7 issues

Volume 21, 6 issues

Volume 20, 6 issues

Volume 19, 6 issues

Volume 18, 5 issues

Volume 17, 5 issues

Volume 16, 4 issues

Volume 15, 4 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 5 issues

Volume 11, 4 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 3 issues

Volume 7, 2 issues

Volume 6, 2 issues

Volume 5, 2 issues

Volume 4, 1 issue

Volume 3, 1 issue

Volume 2, 1 issue

Volume 1, 1 issue

The Journal
About the Journal
Editorial Board
Editorial Interests
Editorial Procedure
Subscriptions
 
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
 
ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Author Index
To Appear
 
Other MSP Journals
Some finiteness results for groups of automorphisms of manifolds

Alexander Kupers

Geometry & Topology 23 (2019) 2277–2333
Bibliography
1 T Akita, Homological infiniteness of Torelli groups, Topology 40 (2001) 213 MR1808217
2 P L Antonelli, D Burghelea, P J Kahn, The nonfinite type of some Diff0Mn, Bull. Amer. Math. Soc. 76 (1970) 1246 MR271982
3 P Antonelli, D Burghelea, P J Kahn, Concordance-homotopy groups and the noninfinite type of some Diff0Mn, Bull. Amer. Math. Soc. 77 (1971) 719 MR282371
4 A Berglund, I Madsen, Rational homotopy theory of automorphisms of manifolds, preprint (2014) arXiv:1401.4096
5 C F Bödigheimer, Configuration models for moduli spaces of Riemann surfaces with boundary, Abh. Math. Sem. Univ. Hamburg 76 (2006) 191 MR2293442
6 A Borel, Stable real cohomology of arithmetic groups, Ann. Sci. École Norm. Sup. 7 (1974) 235 MR0387496
7 B Botvinnik, N Perlmutter, Stable moduli spaces of high-dimensional handlebodies, J. Topol. 10 (2017) 101 MR3653064
8 P Boavida de Brito, M Weiss, Manifold calculus and homotopy sheaves, Homology Homotopy Appl. 15 (2013) 361 MR3138384
9 P Boavida de Brito, M Weiss, Spaces of smooth embeddings and configuration categories, J. Topol. 11 (2018) 65 MR3784227
10 D Burghelea, The rational homotopy groups of Diff(M) and Homeo(Mn) in the stability range, from: "Algebraic topology, Aarhus 1978" (editors J L Dupont, I H Madsen), Lecture Notes in Math. 763, Springer (1979) 604 MR561241
11 D Burghelea, R Lashof, The homotopy type of the space of diffeomorphisms, I, Trans. Amer. Math. Soc. 196 (1974) 1 MR356103
12 D Burghelea, R Lashof, The homotopy type of the space of diffeomorphisms, II, Trans. Amer. Math. Soc. 196 (1974) 37 MR356103
13 D Burghelea, R Lashof, M Rothenberg, Groups of automorphisms of manifolds, 473, Springer (1975) MR0380841
14 J Cerf, La stratification naturelle des espaces de fonctions différentiables réelles et le théorème de la pseudo-isotopie, Inst. Hautes Études Sci. Publ. Math. 39 (1970) 5 MR0292089
15 D Crowley, T Schick, The Gromoll filtration, KO–characteristic classes and metrics of positive scalar curvature, Geom. Topol. 17 (2013) 1773 MR3073935
16 D Crowley, T Schick, W Steimle, Harmonic spinors and metrics of positive curvature via the Gromoll filtration and Toda brackets, preprint (2016) arXiv:1612.04660
17 W G Dwyer, Twisted homological stability for general linear groups, Ann. of Math. 111 (1980) 239 MR569072
18 J Ebert, O Randal-Williams, Generalised Miller–Morita–Mumford classes for block bundles and topological bundles, Algebr. Geom. Topol. 14 (2014) 1181 MR3180831
19 J Ebert, O Randal-Williams, Torelli spaces of high-dimensional manifolds, J. Topol. 8 (2015) 38 MR3335248
20 J Ebert, O Randal-Williams, Semisimplicial spaces, Algebr. Geom. Topol. 19 (2019) 2099 MR3995026
21 N E Enkelmann, W Lück, M Pieper, M Ullmann, C Winges, On the Farrell–Jones conjecture for Waldhausen’s A–theory, Geom. Topol. 22 (2018) 3321 MR3858766
22 F T Farrell, W C Hsiang, On the rational homotopy groups of the diffeomorphism groups of discs, spheres and aspherical manifolds, from: "Algebraic and geometric topology, I" (editor R J Milgram), Proc. Sympos. Pure Math. XXXII, Amer. Math. Soc. (1978) 325 MR520509
23 M H Freedman, F Quinn, Topology of 4–manifolds, 39, Princeton Univ. Press (1990) MR1201584
24 S Galatius, O Randal-Williams, Stable moduli spaces of high-dimensional manifolds, Acta Math. 212 (2014) 257 MR3207759
25 S Galatius, O Randal-Williams, Abelian quotients of mapping class groups of highly connected manifolds, Math. Ann. 365 (2016) 857 MR3498929
26 S Galatius, O Randal-Williams, Homological stability for moduli spaces of high dimensional manifolds, I, J. Amer. Math. Soc. 31 (2018) 215 MR3718454
27 P G Goerss, J F Jardine, Simplicial homotopy theory, 174, Birkhäuser (1999) MR1711612
28 T G Goodwillie, J R Klein, Multiple disjunction for spaces of smooth embeddings, J. Topol. 8 (2015) 651 MR3394312
29 T G Goodwillie, M Weiss, Embeddings from the point of view of immersion theory, II, Geom. Topol. 3 (1999) 103 MR1694808
30 A Gramain, Le type d’homotopie du groupe des difféomorphismes d’une surface compacte, Ann. Sci. École Norm. Sup. 6 (1973) 53 MR0326773
31 A Haefliger, V Poenaru, La classification des immersions combinatoires, Inst. Hautes Études Sci. Publ. Math. 23 (1964) 75 MR0172296
32 I Hambleton, L R Taylor, A guide to the calculation of the surgery obstruction groups for finite groups, from: "Surveys on surgery theory, I" (editors S Cappell, A Ranicki, J Rosenberg), Ann. of Math. Stud. 145, Princeton Univ. Press (2000) 225 MR1747537
33 A Hatcher, Homeomorphisms of sufficiently large P2–irreducible 3–manifolds, Topology 15 (1976) 343 MR0420620
34 A E Hatcher, Concordance spaces, higher simple-homotopy theory, and applications, from: "Algebraic and geometric topology, I" (editor R J Milgram), Proc. Sympos. Pure Math. XXXII, Amer. Math. Soc. (1978) 3 MR520490
35 A E Hatcher, A proof of the Smale conjecture, Diff(S3) O(4), Ann. of Math. 117 (1983) 553 MR701256
36 A Hatcher, On triangulations of surfaces, Topology Appl. 40 (1991) 189 MR1123262
37 A Hatcher, D McCullough, Finiteness of classifying spaces of relative diffeomorphism groups of 3–manifolds, Geom. Topol. 1 (1997) 91 MR1486644
38 A Hatcher, K Vogtmann, Cerf theory for graphs, J. London Math. Soc. 58 (1998) 633 MR1678155
39 A Hatcher, J Wagoner, Pseudo-isotopies of compact manifolds, 6, Soc. Mat. de France (1973) MR0353337
40 H Hendriks, F Laudenbach, Difféomorphismes des sommes connexes en dimension trois, Topology 23 (1984) 423 MR780734
41 A Henriques, D Gepner, Homotopy theory of orbispaces, preprint (2007) arXiv:math/0701916
42 G Hirsch, Sur les groupes d’homologie des espaces fibrés, Bull. Soc. Math. Belgique 6 (1953) 79 MR70174
43 W C Hsiang, R W Sharpe, Parametrized surgery and isotopy, Pacific J. Math. 67 (1976) 401 MR494165
44 K Igusa, The stability theorem for smooth pseudoisotopies, K–Theory 2 (1988) 1 MR972368
45 K Igusa, Higher Franz–Reidemeister torsion, 31, Amer. Math. Soc. (2002) MR1945530
46 N V Ivanov, Groups of diffeomorphisms of Waldhausen manifolds, Zap. Naučn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. 66 (1976) 172 MR0448370
47 J Kalliongis, D McCullough, Isotopies of 3–manifolds, Topology Appl. 71 (1996) 227 MR1397944
48 M A Kervaire, J W Milnor, Groups of homotopy spheres, I, Ann. of Math. 77 (1963) 504 MR0148075
49 R C Kirby, L C Siebenmann, Foundational essays on topological manifolds, smoothings, and triangulations, 88, Princeton Univ. Press (1977) MR0645390
50 M Kreck, Isotopy classes of diffeomorphisms of (k1)–connected almost-parallelizable 2k–manifolds, from: "Algebraic topology, Aarhus 1978" (editors J L Dupont, I H Madsen), Lecture Notes in Math. 763, Springer (1979) 643 MR561244
51 N H Kuiper, Problems concerning manifolds, from: "Manifolds" (editor N H Kuiper), Springer (1971) MR0278311
52 A O Kuku, Some finiteness results in the higher K–theory of orders and group-rings, Topology Appl. 25 (1987) 185 MR884542
53 R Lashof, Embedding spaces, Illinois J. Math. 20 (1976) 144 MR0388403
54 T C Lawson, Some examples of nonfinite diffeomorphism groups, Proc. Amer. Math. Soc. 34 (1972) 570 MR298697
55 J A Lees, Immersions and surgeries of topological manifolds, Bull. Amer. Math. Soc. 75 (1969) 529 MR239602
56 J Levine, Inertia groups of manifolds and diffeomorphisms of spheres, Amer. J. Math. 92 (1970) 243 MR266243
57 I Madsen, R J Milgram, The classifying spaces for surgery and cobordism of manifolds, 92, Princeton Univ. Press (1979) MR548575
58 J P May, The geometry of iterated loop spaces, 271, Springer (1972) MR0420610
59 J McCleary, A user’s guide to spectral sequences, 58, Cambridge Univ. Press (2001) MR1793722
60 P W Michor, Manifolds of differentiable mappings, 3, Shiva (1980) MR583436
61 J G Miller, Homotopy groups of diffeomorphism groups, Indiana Univ. Math. J. 24 (1974/75) 719 MR0362355
62 J Milnor, On spaces having the homotopy type of a CW–complex, Trans. Amer. Math. Soc. 90 (1959) 272 MR100267
63 J Milnor, Lectures on the h–cobordism theorem, Princeton Univ. Press (1965) MR0190942
64 I Moerdijk, J A Svensson, The equivariant Serre spectral sequence, Proc. Amer. Math. Soc. 118 (1993) 263 MR1123662
65 S P Novikov, Homotopy properties of the group of diffeomorphisms of the sphere, Dokl. Akad. Nauk SSSR 148 (1963) 32 MR0144356
66 N Perlmutter, Homological stability for diffeomorphism groups of high-dimensional handlebodies, Algebr. Geom. Topol. 18 (2018) 2769 MR3848399
67 F Quinn, A geometric formulation of surgery, from: "Topology of manifolds" (editors J C Cantrell, J C. H. Edwards), Markham (1970) 500 MR0282375
68 F Quinn, Isotopy of 4–manifolds, J. Differential Geom. 24 (1986) 343 MR868975
69 O Randal-Williams, An upper bound for the pseudoisotopy stable range, Math. Ann. 368 (2017) 1081 MR3673647
70 C P Rourke, Embedded handle theory, concordance and isotopy, from: "Topology of manifolds" (editors J C Cantrell, J C. H. Edwards), Markham (1970) 431 MR0279816
71 D Ruberman, An obstruction to smooth isotopy in dimension 4, Math. Res. Lett. 5 (1998) 743 MR1671187
72 G Segal, Categories and cohomology theories, Topology 13 (1974) 293 MR0353298
73 J P Serre, Groupes d’homotopie et classes de groupes abéliens, Ann. of Math. 58 (1953) 258 MR0059548
74 J P Serre, Arithmetic groups, from: "Homological group theory" (editor C T C Wall), London Math. Soc. Lecture Note Ser. 36, Cambridge Univ. Press (1979) 105 MR564421
75 L C Siebenmann, Deformation of homeomorphisms on stratified sets, Comment. Math. Helv. 47 (1972) 123 MR0319207
76 D P Sinha, Manifold-theoretic compactifications of configuration spaces, Selecta Math. 10 (2004) 391 MR2099074
77 S Smale, The classification of immersions of spheres in Euclidean spaces, Ann. of Math. 69 (1959) 327 MR0105117
78 S Smale, Diffeomorphisms of the 2–sphere, Proc. Amer. Math. Soc. 10 (1959) 621 MR112149
79 K Strebel, Quadratic differentials, 5, Springer (1984) MR743423
80 D Sullivan, Infinitesimal computations in topology, Inst. Hautes Études Sci. Publ. Math. 47 (1977) 269 MR0646078
81 G Triantafillou, Automorphisms of spaces with finite fundamental group, Trans. Amer. Math. Soc. 347 (1995) 3391 MR1316864
82 F Waldhausen, Algebraic K–theory of spaces, from: "Algebraic and geometric topology" (editors A Ranicki, N Levitt, F Quinn), Lecture Notes in Math. 1126, Springer (1985) 318 MR802796
83 F Waldhausen, B Jahren, J Rognes, Spaces of PL manifolds and categories of simple maps, 186, Princeton Univ. Press (2013) MR3202834
84 C T C Wall, Classification problems in differential topology, III : Applications to special cases, Topology 3 (1965) 291 MR0177421
85 T Watanabe, On Kontsevich’s characteristic classes for higher dimensional sphere bundles, I : The simplest class, Math. Z. 262 (2009) 683 MR2506314
86 T Watanabe, On Kontsevich’s characteristic classes for higher-dimensional sphere bundles, II : Higher classes, J. Topol. 2 (2009) 624 MR2546588
87 M Weiss, Embeddings from the point of view of immersion theory, I, Geom. Topol. 3 (1999) 67 MR1694812
88 M S Weiss, Dalian notes on rational Pontryagin classes, preprint (2015) arXiv:1507.00153