Geodesic
About three conjectures on finite group actions on 3-manifolds
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 12 (2015), pp. 955-959.

Voir la notice de l'article provenant de la source Math-Net.Ru

We give a survey centering around three conjectures on finite group actions on homology 3-spheres, and also on actions on closed 3-manifolds containing a hyperelliptic rotation.
Keywords: Finite group action, 3-manifold, homology 3-sphere
Mots-clés : hyperelliptic rotation. 
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Bruno P. Zimmermann. About three conjectures on finite group actions on 3-manifolds. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 12 (2015), pp. 955-959. http://geodesic.mathdoc.fr/item/SEMR_2015_12_a49/

[1] M. Boileau, L. Paoluzzi, B. Zimmermann, “A characterisation of $S^3$ among homology spheres”, Geom. Topol. Monographs, 14, 2008, 83–103 | DOI | MR | Zbl

[2] W. Chen, S. Kwasik, R. Schultz, Finite symmetries of $S^4$, arXiv: 1412.5901

[3] R. M. Dotzel, G. C. Hamrick, “$p$-group actions on homology spheres”, Invent. math., 62:3 (1981), 437–442 | DOI | MR | Zbl

[4] C. McA. Gordon, “Some aspects of classical knot theory”, Knot Theory, Proceedings (Plans-sur-Bex, Switzerland), Lect. Notes Math., 685, ed. J. C. Hausmann, Springer, 1977, 1–60 | MR

[5] D. Gorenstein, The classification of finite simple groups, Plenum Press, New York, 1983 | MR | Zbl

[6] G. A. Jones, A. D. Mednykh, Three-dimensional hyperbolic manifolds with a large isometry group, Preprint

[7] A. Kawauchi, “Topological imitations”, Lectures at Knots, 96, ed. Shin'ichi Suzuki, World Scientific Publ. Co., 1997, 19–37 pp. | MR | Zbl

[8] A. Kawauchi, “Topological imitation and Reni–Mecchia–Zimmermann's conjecture”, Kyungpook Math. J., 46:1 (2006), 1–9 | MR | Zbl

[9] R. Lee, “Semicharacteristic classes”, Topology, 12 (1973), 183–199 | DOI | MR | Zbl

[10] M. Mecchia, “Finite groups acting on 3-manifolds and cyclic branched coverings of knots”, Geom. Topol. Monogr., 14, 2008, 393–416 | DOI | MR | Zbl

[11] M. Mecchia, B. Zimmermann, “On finite groups acting on $\mathbb{Z_2}$-homology 3-spheres”, Math. Z., 248:4 (2004), 675–693 | DOI | MR | Zbl

[12] M. Mecchia, B. Zimmermann, “On finite simple and nonsolvable groups acting on homology 4-spheres”, Top. Appl., 153:15 (2006), 2933–2942 | DOI | MR | Zbl

[13] M. Mecchia, B. Zimmermann, “On finite groups acting on homology 4-spheres and finite subgroups of ${\rm SO}(5)$”, Top. Appl., 158:6 (2011), 741–747 | DOI | MR | Zbl

[14] M. Mecchia, B. Zimmermann, “The number of knots and links with the same 2-fold branched covering”, Quart. J. Math., 55:1 (2004), 69–76 | DOI | MR | Zbl

[15] M. Mecchia, B. Zimmermann, “On finite simple groups acting on integer and mod 2 homology 3-spheres”, J. Algebra, 298:2 (2006), 460–467 | DOI | MR | Zbl

[16] R. J. Milgram, “Evaluating the Swan finiteness obstruction for finite groups”, Algebraic and Geometric Topology, Lecture Notes in Math., 1126, Springer, 127–158, 1985 | MR

[17] J. Milnor, “Groups which act on $S^n$ without fixed points”, Amer. J. Math., 79 (1957), 623–630 | DOI | MR | Zbl

[18] M. Reni, B. Zimmermann, “Finite simple groups acting on 3-manifolds and homology spheres”, Rend. Ist. Mat. Univ. Trieste, 32:1, suppl. (2001), 305–315 http://rendiconti.dmi.units.it | MR | Zbl

[19] M. Suzuki, Group Theory, v. II, Springer-Verlag, 1982 | MR | Zbl

[20] B. Zimmermann, “On the classification of finite groups acting on homology 3-spheres”, Pacific J. Math., 217:2 (2004), 387–395 | DOI | MR | Zbl

[21] B. Zimmermann, “On finite simple groups acting on homology spheres with small fixed point sets”, Bol. Soc. Mat. Mex., 20:2 (2014), 611–621 | DOI | MR | Zbl

[22] B. Zimmermann, “Cyclic branched coverings and homology 3-spheres with large group actions”, Fund. Math., 184 (2004), 343–353 | DOI | MR | Zbl

[23] B. Zimmermann, “On finite simple groups acting on homology 3-spheres”, Topology Appl., 125:2 (2002), 199–202 | DOI | MR | Zbl