Geodesic
Smooth Actions of $p$-Toral Groups on $\mathbb Z$-Acyclic Manifolds
Informatics and Automation, Algebraic topology, combinatorics, and mathematical physics, Tome 305 (2019), pp. 283-290.

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

For a $p$-toral group $G$, we answer the question which compact (respectively, open) smooth manifolds $M$ can be diffeomorphic to the fixed point sets of smooth actions of $G$ on compact (respectively, open) smooth manifolds $E$ of the homotopy type of a finite $\mathbb Z$-acyclic CW complex admitting a cellular map of period $p$, with exactly one fixed point. In the case where the CW complex is contractible, $E$ can be chosen to be a disk (respectively, Euclidean space). 
@article{TRSPY_2019_305_a14,
     author = {Krzysztof M. Pawa{\l}owski and Jan Pulikowski},
     title = {Smooth {Actions} of $p${-Toral} {Groups} on $\mathbb Z${-Acyclic} {Manifolds}},
     journal = {Informatics and Automation},
     pages = {283--290},
     publisher = {mathdoc},
     volume = {305},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TRSPY_2019_305_a14/}
}
TY  - JOUR
AU  - Krzysztof M. Pawałowski
AU  - Jan Pulikowski
TI  - Smooth Actions of $p$-Toral Groups on $\mathbb Z$-Acyclic Manifolds
JO  - Informatics and Automation
PY  - 2019
SP  - 283
EP  - 290
VL  - 305
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TRSPY_2019_305_a14/
LA  - ru
ID  - TRSPY_2019_305_a14
ER  - 
%0 Journal Article
%A Krzysztof M. Pawałowski
%A Jan Pulikowski
%T Smooth Actions of $p$-Toral Groups on $\mathbb Z$-Acyclic Manifolds
%J Informatics and Automation
%D 2019
%P 283-290
%V 305
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TRSPY_2019_305_a14/
%G ru
%F TRSPY_2019_305_a14
Krzysztof M. Pawałowski; Jan Pulikowski. Smooth Actions of $p$-Toral Groups on $\mathbb Z$-Acyclic Manifolds. Informatics and Automation, Algebraic topology, combinatorics, and mathematical physics, Tome 305 (2019), pp. 283-290. http://geodesic.mathdoc.fr/item/TRSPY_2019_305_a14/

[1] Assadi A.H., Finite group actions on simply-connected manifolds and CW complexes, Mem. AMS, 35, N 257, Amer. Math. Soc., Providence, RI, 1982

[2] Assadi A., Browder W., “On the existence and classification of extensions of actions on submanifolds of disks and spheres”, Trans. Amer. Math. Soc., 291 (1985), 487–502 | DOI | Zbl

[3] M. F. Atiyah, K-Theory, W. A. Benjamin, New York, 1967 | Zbl

[4] G. E. Bredon, Introduction to Compact Transformation Groups, Pure Appl. Math., 46, Academic, New York, 1972 | Zbl

[5] Edmonds A.L., Lee R., “Fixed point sets of group actions on Euclidean space”, Topology, 14 (1975), 339–345 | DOI | Zbl

[6] Jones L., “The converse to the fixed point theorem of P.A. Smith. I”, Ann. Math. Ser. 2, 94 (1971), 52–68 | DOI | Zbl

[7] Oliver R., “Fixed point sets and tangent bundles of actions on disks and Euclidean spaces”, Topology, 35 (1996), 583–615 | DOI | Zbl

[8] Pawałowski K., “Fixed point sets of smooth group actions on disks and Euclidean spaces”, Topology, 28 (1989), 273–289 ; “Corrections”, Topology, 35 (1996), 749–750 | DOI | Zbl | DOI | Zbl

[9] Pawałowski K., “Manifolds as fixed point sets of smooth compact Lie group actions”, Current trends in transformation groups, $K$-Monogr. Math., 7, Kluwer, Dordrecht, 2002, 79–104 | DOI | Zbl