Some results and conjectures on finite groups acting on homology spheres
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 2 (2005), pp. 233-238.

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

This is a note based on a talk given in the Workshop on geometry and topology of $3$-manifolds, Novosibirsk, 22–26 August 2005. We consider the class of finite groups, which admit arbitrary, i.e. not necessarily free actions on integer and $\bmod2$ homology spheres, with an emphasis on the $3$- and $4$-dimensional cases. We recall some classical results and present some recent progress as well as new results, open problems and the emerging conjectural picture of the situation.
@article{SEMR_2005_2_a16,
     author = {B. P. Zimmermann},
     title = {Some results and conjectures on finite groups acting on homology spheres},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {233--238},
     publisher = {mathdoc},
     volume = {2},
     year = {2005},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2005_2_a16/}
}
TY  - JOUR
AU  - B. P. Zimmermann
TI  - Some results and conjectures on finite groups acting on homology spheres
JO  - Sibirskie èlektronnye matematičeskie izvestiâ
PY  - 2005
SP  - 233
EP  - 238
VL  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SEMR_2005_2_a16/
LA  - en
ID  - SEMR_2005_2_a16
ER  - 
%0 Journal Article
%A B. P. Zimmermann
%T Some results and conjectures on finite groups acting on homology spheres
%J Sibirskie èlektronnye matematičeskie izvestiâ
%D 2005
%P 233-238
%V 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SEMR_2005_2_a16/
%G en
%F SEMR_2005_2_a16
B. P. Zimmermann. Some results and conjectures on finite groups acting on homology spheres. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 2 (2005), pp. 233-238. http://geodesic.mathdoc.fr/item/SEMR_2005_2_a16/

[1] A. Adem, R. J. Milgram, Cohomology of Finite Groups, Grundlehren der mathematischen Wissenschaften, 309, Springer, 1994 | MR | Zbl

[2] G. Bredon, Introduction to compact Transformation Groups, Academic Press, New York, 1972 | MR | Zbl

[3] K. S. Brown, Cohomology of Groups, Graduate Texts in Mathematics, 87, Springer, 1982 | MR

[4] D. Cooper, D. D. Long, “Free actions of finite groups on rational homology 3-spheres”, Top. Appl., 101 (2000), 143–148 | DOI | MR | Zbl

[5] R. M. Dotzel, “Orientation preserving actions of finite abelian groups on spheres”, Proc. Amer. Math. Soc., 100 (1987), 159–163 | MR | Zbl

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

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

[8] I. Madsen, C. B. Thomas, C. T. C. Wall, “The topological space form problem II: Existence of free actions”, Topology, 15 (1976), 375–382 | DOI | MR | Zbl

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

[10] M. Mecchia, B. Zimmermann, On finite simple and nonsolvable groups acting on homology 4-spheres, arXiv: math/0604239 | MR

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

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

[13] W. Pardon, “Mod 2 semi-characteristics and the converse of a theorem of Milnor”, Math. Z, 171 (1980), 247–268 | DOI | MR | Zbl

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

[15] J. Wolf, Spaces of Constant Curvature, Publish or Perish, Boston, 1974 | MR

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

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