Volume 15, issue 6 (2015)

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

Volume 25
Issue 7, 3789–4436
Issue 6, 3145–3787
Issue 5, 2527–3144
Issue 4, 1917–2526
Issue 3, 1265–1915
Issue 2, 645–1264
Issue 1, 1–644

Volume 24, 9 issues

Volume 23, 9 issues

Volume 22, 8 issues

Volume 21, 7 issues

Volume 20, 7 issues

Volume 19, 7 issues

Volume 18, 7 issues

Volume 17, 6 issues

Volume 16, 6 issues

Volume 15, 6 issues

Volume 14, 6 issues

Volume 13, 6 issues

Volume 12, 4 issues

Volume 11, 5 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 4 issues

Volume 7, 4 issues

Volume 6, 5 issues

Volume 5, 4 issues

Volume 4, 2 issues

Volume 3, 2 issues

Volume 2, 2 issues

Volume 1, 2 issues

The Journal
About the journal
Ethics and policies
Peer-review process
 
Submission guidelines
Submission form
Editorial board
 
Subscriptions
 
ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
 
Author index
To appear
 
Other MSP journals
Fixed-point free circle actions on $4$–manifolds

Weimin Chen

Algebraic & Geometric Topology 15 (2015) 3253–3303
Bibliography
1 K Asano, Homeomorphisms of prism manifolds, Yokohama Math. J. 26 (1978) 19 MR524878
2 S J Baldridge, Seiberg–Witten invariants, orbifolds, and circle actions, Trans. Amer. Math. Soc. 355 (2003) 1669 MR1946410
3 S Baldridge, Seiberg–Witten vanishing theorem for $S^1$–manifolds with fixed points, Pacific J. Math. 217 (2004) 1 MR2105762
4 M Boileau, B Leeb, J Porti, Geometrization of $3$–dimensional orbifolds, Ann. of Math. 162 (2005) 195 MR2178962
5 M Boileau, S Maillot, J Porti, Three-dimensional orbifolds and their geometric structures, Panoramas et Synthèses 15, Soc. Math. France (2003) MR2060653
6 M Boileau, J P Otal, Scindements de Heegaard et groupe des homéotopies des petites variétés de Seifert, Invent. Math. 106 (1991) 85 MR1123375
7 F Bonahon, Difféotopies des espaces lenticulaires, Topology 22 (1983) 305 MR710104
8 S Cappell, S Weinberger, M Yan, Closed aspherical manifolds with center, J. Topol. 6 (2013) 1009 MR3145148
9 A Casson, D Jungreis, Convergence groups and Seifert fibered $3$–manifolds, Invent. Math. 118 (1994) 441 MR1296353
10 W Chen, On a notion of maps between orbifolds, II: Homotopy and CW–complex, Commun. Contemp. Math. 8 (2006) 763 MR2274941
11 W Chen, Seiberg–Witten invariants of $3$–orbifolds and non-Kähler surfaces, J. Gökova Geom. Topol. GGT 6 (2012) 1 MR3011643
12 W Chen, Hurwitz-type bound, knot surgery, and smooth $\mathbb{S}^1$–four-manifolds, Math. Z. 276 (2014) 267 MR3150204
13 W Dicks, M J Dunwoody, Groups acting on graphs, Cambridge Studies in Advanced Mathematics 17, Cambridge Univ. Press (1989) MR1001965
14 J Dinkelbach, B Leeb, Equivariant Ricci flow with surgery and applications to finite group actions on geometric 3–manifolds, Geom. Topol. 13 (2009) 1129 MR2491658
15 W D Dunbar, Nonfibering spherical $3$–orbifolds, Trans. Amer. Math. Soc. 341 (1994) 121 MR1118824
16 R Fintushel, Locally smooth circle actions on homotopy $4$–spheres, Duke Math. J. 43 (1976) 63 MR0394716
17 R Fintushel, Circle actions on simply connected $4$–manifolds, Trans. Amer. Math. Soc. 230 (1977) 147 MR0458456
18 R Fintushel, Classification of circle actions on $4$–manifolds, Trans. Amer. Math. Soc. 242 (1978) 377 MR496815
19 R Fintushel, R J Stern, Immersed spheres in $4$–manifolds and the immersed Thom conjecture, Turkish J. Math. 19 (1995) 145 MR1349567
20 D Gabai, Convergence groups are Fuchsian groups, Ann. of Math. 136 (1992) 447 MR1189862
21 A Haefliger, Homotopy and integrability, from: "Manifolds" (editor N H Kuiper), Lecture Notes in Mathematics 197, Springer (1971) 133 MR0285027
22 A Haefliger, Groupoïdes d'holonomie et classifiants, from: "Transversal structure of foliations" (1984) 70 MR755163
23 A Hatcher, On the diffeomorphism group of $S^{1}\times S^{2}$, Proc. Amer. Math. Soc. 83 (1981) 427 MR624946
24 J Hempel, $3$–manifolds, Ann. of Math. Studies 86, Princeton Univ. Press (1976) MR0415619
25 J A Hillman, Four-manifolds, geometries and knots, Geometry & Topology Monographs 5 (2002) MR1943724
26 C Hodgson, J H Rubinstein, Involutions and isotopies of lens spaces, from: "Knot theory and manifolds" (editor D Rolfsen), Lecture Notes in Math. 1144, Springer (1985) 60 MR823282
27 B Kleiner, J Lott, Notes on Perelman's papers, arXiv:math.DG/0605667
28 K B Lee, F Raymond, The role of Seifert fiber spaces in transformation groups, from: "Group actions on manifolds" (editor R Schultz), Contemp. Math. 36, Amer. Math. Soc. (1985) 367 MR780974
29 A M Macbeath, Geometrical realization of isomorphisms between plane groups, Bull. Amer. Math. Soc. 71 (1965) 629 MR0177110
30 W Magnus, A Karrass, D Solitar, Combinatorial group theory: presentations of groups in terms of generators and relations, Interscience (1966) MR0207802
31 D McCullough, A Miller, Manifold covers of $3$–orbifolds with geometric pieces, Topology Appl. 31 (1989) 169 MR994409
32 W H Meeks III, P Scott, Finite group actions on $3$–manifolds, Invent. Math. 86 (1986) 287 MR856847
33 W H Meeks III, S T Yau, Topology of three-dimensional manifolds and the embedding problems in minimal surface theory, Ann. of Math. 112 (1980) 441 MR595203
34 G Meng, C H Taubes, $\underline{\mathrm{SW}}=$ Milnor torsion, Math. Res. Lett. 3 (1996) 661 MR1418579
35 P S Pao, Nonlinear circle actions on the $4$–sphere and twisting spun knots, Topology 17 (1978) 291 MR508892
36 G Perelman, The entropy formula for the Ricci flow and its geometric applications, arXiv:math/0211159
37 C Petronio, Spherical splitting of $3$–orbifolds, Math. Proc. Cambridge Philos. Soc. 142 (2007) 269 MR2314601
38 E Rips, Z Sela, Cyclic splittings of finitely presented groups and the canonical JSJ decomposition, Ann. of Math. 146 (1997) 53 MR1469317
39 J H Rubinstein, On $3$–manifolds that have finite fundamental group and contain Klein bottles, Trans. Amer. Math. Soc. 251 (1979) 129 MR531972
40 J H Rubinstein, J S Birman, One-sided Heegaard splittings and homeotopy groups of some $3$–manifolds, Proc. London Math. Soc. 49 (1984) 517 MR759302
41 P Scott, The geometries of $3$–manifolds, Bull. London Math. Soc. 15 (1983) 401 MR705527
42 P Scott, T Wall, Topological methods in group theory, from: "Homological group theory" (editor C T C Wall), London Math. Soc. Lecture Note Ser. 36, Cambridge Univ. Press (1979) 137 MR564422
43 Z Sela, Structure and rigidity in (Gromov) hyperbolic groups and discrete groups in rank $1$ Lie groups, II, Geom. Funct. Anal. 7 (1997) 561 MR1466338
44 G A Swarup, On a theorem of C B Thomas, J. London Math. Soc. 8 (1974) 13 MR0341474
45 C B Thomas, The oriented homotopy type of compact $3$–manifolds, Proc. London Math. Soc. 19 (1969) 31 MR0248838
46 V G Turaev, Towards the topological classification of geometric $3$–manifolds, from: "Topology and geometry — Rohlin Seminar" (editor O Y Viro), Lecture Notes in Math. 1346, Springer (1988) 291 MR970081
47 V Turaev, A combinatorial formulation for the Seiberg–Witten invariants of $3$–manifolds, Math. Res. Lett. 5 (1998) 583 MR1666856
48 T Yoshida, Simply connected smooth $4$–manifolds which admit nontrivial smooth $S^{1}$ actions, Math. J. Okayama Univ. 20 (1978) 25 MR0494173