Algebraic & Geometric Topology Volume 9, issue 3 (2009)

Download this article
	For screen
	For printing

Recent Issues

The Journal

About the Journal

Editorial Board

Submission Guidelines

Submission Page

Policies for Authors

Ethics Statement

ISSN 1472-2739 (online)

ISSN 1472-2747 (print)

Other MSP Journals

Finiteness of mapping degrees and ${\rm PSL}(2,\mathbf{R})$–volume on graph manifolds

Pierre Derbez and Shicheng Wang

Algebraic & Geometric Topology 9 (2009) 1727–1749

DOI: 10.2140/agt.2009.9.1727

Bibliography

1	R Brooks, W Goldman, The Godbillon–Vey invariant of a transversely homogeneous foliation, Trans. Amer. Math. Soc. 286 (1984) 651 MR760978
2	R Brooks, W Goldman, Volumes in Seifert space, Duke Math. J. 51 (1984) 529 MR757951
3	J A Carlson, D Toledo, Harmonic mappings of Kähler manifolds to locally symmetric spaces, Inst. Hautes Études Sci. Publ. Math. (1989) 173 MR1019964
4	C Connell, B Farb, The degree theorem in higher rank, J. Differential Geom. 65 (2003) 19 MR2057530
5	P Derbez, Topological rigidity and Gromov simplicial volume, to appear in Comment. Math. Helv. arXiv:math.GT/0607766
6	P Derbez, Nonzero degree maps between closed orientable three-manifolds, Trans. Amer. Math. Soc. 359 (2007) 3887 MR2302517
7	M Gromov, Volume and bounded cohomology, Inst. Hautes Études Sci. Publ. Math. (1982) MR686042
8	W H Jaco, P B Shalen, Seifert fibered spaces in $3$–manifolds, Mem. Amer. Math. Soc. 21 (1979) MR539411
9	J F Lafont, B Schmidt, Simplicial volume of closed locally symmetric spaces of non-compact type, Acta Math. 197 (2006) 129 MR2285319
10	J Luecke, Y Q Wu, Relative Euler number and finite covers of graph manifolds, from: "Geometric topology (Athens, GA, 1993)" (editor W H Kazez), AMS/IP Stud. Adv. Math. 2, Amer. Math. Soc. (1997) 80 MR1470722
11	J Milnor, W Thurston, Characteristic numbers of $3$–manifolds, Enseignement Math. $(2)$ 23 (1977) 249 MR0500978
12	A Reznikov, Volumes of discrete groups and topological complexity of homology spheres, Math. Ann. 306 (1996) 547 MR1415078
13	W P Thurston, Three-dimensional manifolds, Kleinian groups and hyperbolic geometry, Bull. Amer. Math. Soc. $($N.S.$)$ 6 (1982) 357 MR648524
14	S Wang, The $\pi_1$–injectivity of self-maps of nonzero degree on $3$–manifolds, Math. Ann. 297 (1993) 171 MR1238414
15	S Wang, Non-zero degree maps between 3-manifolds, from: "Proceedings of the International Congress of Mathematicians, Vol. II (Beijing, 2002)", Higher Ed. Press (2002) 457 MR1957056
16	S Wang, Q Zhou, Any $3$–manifold $1$–dominates at most finitely many geometric $3$–manifolds, Math. Ann. 322 (2002) 525 MR1895705
17	F Yu, S Wang, Covering degrees are determined by graph manifolds involved, Comment. Math. Helv. 74 (1999) 238 MR1691948