Volume 14 (2008)

Download this article
For screen
For printing
Recent Volumes
Volume 1, 1998
Volume 2, 1999
Volume 3, 2000
Volume 4, 2002
Volume 5, 2002
Volume 6, 2003
Volume 7, 2004
Volume 8, 2006
Volume 9, 2006
Volume 10, 2007
Volume 11, 2007
Volume 12, 2007
Volume 13, 2008
Volume 14, 2008
Volume 15, 2008
Volume 16, 2009
Volume 17, 2011
Volume 18, 2012
Volume 19, 2015
The Series
About this Series
Ethics Statement
Purchase Printed Copies
Author Index
ISSN (electronic): 1464-8997
ISSN (print): 1464-8989
 
MSP Books and Monographs
Other MSP Publications

Finite groups acting on 3–manifolds and cyclic branched coverings of knots

Mattia Mecchia

Geometry & Topology Monographs 14 (2008) 393–416

DOI: 10.2140/gtm.2008.14.393

Bibliography
1 M Boileau, B Leeb, J Porti, Geometrization of 3-dimensional orbifolds, Ann. of Math. (2) 162 (2005) 195–290 MR2178962
2 M Boileau, L Paoluzzi, B Zimmermann, A characterisation of S³ among homology spheres arXiv:math.GT/0606220
3 J H Conway, R T Curtis, S P Norton, R A Parker, R A Wilson, Atlas of finite groups, Oxford University Press (1985) MR827219 Maximal subgroups and ordinary characters for simple groups, With computational assistance from J. G. Thackray
4 D Cooper, D D Long, Free actions of finite groups on rational homology 3-spheres, Topology Appl. 101 (2000) 143–148 MR1732066
5 R M Dotzel, G C Hamrick, p-group actions on homology spheres, Invent. Math. 62 (1981) 437–442 MR604837
6 C M Gordon, Knots whose branched cyclic coverings have periodic homology, Trans. Amer. Math. Soc. 168 (1972) 357–370 MR0295327
7 D Gorenstein, The classification of finite simple groups. Vol. 1, The University Series in Mathematics, Plenum Press (1983) MR746470 Groups of noncharacteristic 2 type
8 D Gorenstein, R Lyons, R Solomon, The classification of the finite simple groups, Mathematical Surveys and Monographs 40, American Mathematical Society (1994) MR1303592
9 D Gorenstein, R Lyons, R Solomon, The classification of the finite simple groups. Number 2. Part I. Chapter G, Mathematical Surveys and Monographs 40, American Mathematical Society (1996) MR1358135 General group theory
10 M Mecchia, How hyperbolic knots with homeomorphic cyclic branched coverings are related, Topology Appl. 121 (2002) 521–533 MR1909006
11 M Mecchia, B Zimmermann, On finite groups acting on Z2-homology 3-spheres, Math. Z. 248 (2004) 675–693 MR2103536
12 M Mecchia, B Zimmermann, On finite simple groups acting on integer and mod 2 homology 3-spheres, J. Algebra 298 (2006) 460–467 MR2217622
13 R J Milgram, Evaluating the Swan finiteness obstruction for periodic groups, from: "Algebraic and geometric topology (New Brunswick, N.J., 1983)", Lecture Notes in Math. 1126, Springer (1985) 127–158 MR802788
14 J Milnor, Groups which act on Sn without fixed points, Amer. J. Math. 79 (1957) 623–630 MR0090056
15 G Perelman, The entropy formula for the Ricci flow and its geometric applications arXiv:math.DG/0211159
16 G Perelman, Ricci flow with surgery on three-manifolds arXiv:math.DG/0303109
17 M Reni, On π-hyperbolic knots with the same 2-fold branched coverings, Math. Ann. 316 (2000) 681–697 MR1758448
18 M Reni, B Zimmermann, Finite simple groups acting on 3-manifolds and homology spheres, Rend. Istit. Mat. Univ. Trieste 32 (2001) MR1893403 Dedicated to the memory of Marco Reni
19 M Reni, B Zimmermann, Hyperbolic 3-manifolds as cyclic branched coverings, Comment. Math. Helv. 76 (2001) 300–313 MR1839348
20 M Reni, B Zimmermann, On hyperelliptic involutions of hyperbolic 3-manifolds, Math. Ann. 321 (2001) 295–317 MR1866490
21 M Sakuma, Homology of abelian coverings of links and spatial graphs, Canad. J. Math. 47 (1995) 201–224 MR1319696
22 M Suzuki, Group theory. I, Grundlehren series 247, Springer (1982) MR648772 Translated from the Japanese by the author
23 M Suzuki, Group theory. II, Grundlehren series 248, Springer (1982) MR815926 Translated from the Japanese by the author
24 W Thurston, The geometry and topology of three-manifolds, Princeton Univ. Math. Dept. Lecture Notes (1979)
25 B Zimmermann, On the classification of finite groups acting on homology 3-spheres, Pacific J. Math. 217 (2004) 387–395 MR2109941