Volume 21, issue 5 (2017)

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

Volume 29, 1 issue Volume 29, 1 issue

Volume 28, 9 issues

Volume 27, 9 issues

Volume 26, 8 issues

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 Procedure
Subscriptions
 
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
 
ISSN 1364-0380 (online)
ISSN 1465-3060 (print)
Author Index
To Appear
 
Other MSP Journals
Positive simplicial volume implies virtually positive Seifert volume for $3$–manifolds

Pierre Derbez, Yi Liu, Hongbin Sun and Shicheng Wang

Geometry & Topology 21 (2017) 3159–3190
Bibliography
1 I Agol, The virtual Haken conjecture, Doc. Math. 18 (2013) 1045 MR3104553
2 G Besson, G Courtois, S Gallot, Inégalités de Milnor–Wood géométriques, Comment. Math. Helv. 82 (2007) 753 MR2341839
3 R Brooks, W Goldman, The Godbillon–Vey invariant of a transversely homogeneous foliation, Trans. Amer. Math. Soc. 286 (1984) 651 MR760978
4 R Brooks, W Goldman, Volumes in Seifert space, Duke Math. J. 51 (1984) 529 MR757951
5 P Derbez, Y Liu, S Wang, Chern–Simons theory, surface separability, and volumes of 3–manifolds, J. Topol. 8 (2015) 933 MR3431665
6 P Derbez, H B Sun, S C Wang, Finiteness of mapping degree sets for 3–manifolds, Acta Math. Sin. (Engl. Ser.) 27 (2011) 807 MR2786444
7 P Derbez, S Wang, Finiteness of mapping degrees and PSL(2, )–volume on graph manifolds, Algebr. Geom. Topol. 9 (2009) 1727 MR2539193
8 P Derbez, S Wang, Graph manifolds have virtually positive Seifert volume, J. Lond. Math. Soc. 86 (2012) 17 MR2959293
9 A Gaifullin, Universal realisators for homology classes, Geom. Topol. 17 (2013) 1745 MR3073934
10 M Gromov, Volume and bounded cohomology, Inst. Hautes Études Sci. Publ. Math. 56 (1982) 5 MR686042
11 F Haglund, D T Wise, Special cube complexes, Geom. Funct. Anal. 17 (2008) 1551 MR2377497
12 W H Jaco, P B Shalen, Seifert fibered spaces in 3–manifolds, 220, Amer. Math. Soc. (1979) MR539411
13 K Johannson, Homotopy equivalences of 3–manifolds with boundaries, 761, Springer (1979) MR551744
14 J Kahn, V Markovic, Immersing almost geodesic surfaces in a closed hyperbolic three manifold, Ann. of Math. 175 (2012) 1127 MR2912704
15 R Kirby, Problems in low dimensional manifold theory, from: "Algebraic and geometric topology, II" (editor R J Milgram), Proc. Sympos. Pure Math. XXXII, Amer. Math. Soc. (1978) 273 MR520548
16 Y Liu, A characterization of virtually embedded subsurfaces in 3–manifolds, Trans. Amer. Math. Soc. 369 (2017) 1237 MR3572272
17 Y Liu, V Markovic, Homology of curves and surfaces in closed hyperbolic 3–manifolds, Duke Math. J. 164 (2015) 2723 MR3417184
18 J Luecke, Y Q Wu, Relative Euler number and finite covers of graph manifolds, from: "Geometric topology" (editor W H Kazez), AMS/IP Stud. Adv. Math. 2, Amer. Math. Soc. (1997) 80 MR1470722
19 W D Neumann, Commensurability and virtual fibration for graph manifolds, Topology 36 (1997) 355 MR1415593
20 P Przytycki, D T Wise, Mixed 3–manifolds are virtually special, preprint (2012) arXiv:1205.6742
21 P Przytycki, D T Wise, Graph manifolds with boundary are virtually special, J. Topol. 7 (2014) 419 MR3217626
22 P Przytycki, D T Wise, Separability of embedded surfaces in 3–manifolds, Compos. Math. 150 (2014) 1623 MR3260144
23 A Reznikov, Rationality of secondary classes, J. Differential Geom. 43 (1996) 674 MR1412681
24 J H Rubinstein, S Wang, π1–injective surfaces in graph manifolds, Comment. Math. Helv. 73 (1998) 499 MR1639876
25 P Scott, The geometries of 3–manifolds, Bull. London Math. Soc. 15 (1983) 401 MR705527
26 T Soma, The Gromov invariant of links, Invent. Math. 64 (1981) 445 MR632984
27 H Sun, Virtual domination of 3–manifolds, Geom. Topol. 19 (2015) 2277 MR3375528
28 W P Thurston, The geometry and topology of three-manifolds, lecture notes (1979)
29 W P Thurston, Three-dimensional manifolds, Kleinian groups and hyperbolic geometry, Bull. Amer. Math. Soc. 6 (1982) 357 MR648524
30 S C Wang, Y Q Wu, Covering invariants and co-Hopficity of 3–manifold groups, Proc. London Math. Soc. 68 (1994) 203 MR1243842
31 D T Wise, From riches to raags : 3–manifolds, right-angled Artin groups, and cubical geometry, 117, Amer. Math. Soc. (2012) MR2986461
32 F Yu, S Wang, Covering degrees are determined by graph manifolds involved, Comment. Math. Helv. 74 (1999) 238 MR1691948