Geodesic
On the Least Number of Fixed Points of an Equivariant Map
Matematičeskie zametki, Tome 69 (2001) no. 1, pp. 100-112.

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

The problem on the least number of fixed points of an equivariant map of a compact polyhedron on which a finite group acts is considered. For such a map, the least number of fixed points and the least number of fixed orbits are estimated in terms of invariants of the type of Nielsen numbers. The estimates obtained are sharp. The results are similar to those of P. Wong, but their assumptions are essentially weaker. Some notations are refined. The proofs are constructive. 
@article{MZM_2001_69_1_a8,
     author = {T. N. Fomenko},
     title = {On the {Least} {Number} of {Fixed} {Points} of an {Equivariant} {Map}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {100--112},
     publisher = {mathdoc},
     volume = {69},
     number = {1},
     year = {2001},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2001_69_1_a8/}
}
TY  - JOUR
AU  - T. N. Fomenko
TI  - On the Least Number of Fixed Points of an Equivariant Map
JO  - Matematičeskie zametki
PY  - 2001
SP  - 100
EP  - 112
VL  - 69
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2001_69_1_a8/
LA  - ru
ID  - MZM_2001_69_1_a8
ER  - 
%0 Journal Article
%A T. N. Fomenko
%T On the Least Number of Fixed Points of an Equivariant Map
%J Matematičeskie zametki
%D 2001
%P 100-112
%V 69
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2001_69_1_a8/
%G ru
%F MZM_2001_69_1_a8
T. N. Fomenko. On the Least Number of Fixed Points of an Equivariant Map. Matematičeskie zametki, Tome 69 (2001) no. 1, pp. 100-112. http://geodesic.mathdoc.fr/item/MZM_2001_69_1_a8/

[1] Jiang B., “On the least number of fixed points”, Amer. J. Math., 102:4 (1980), 749–763 | DOI | MR | Zbl

[2] Schirmer H., “A relative Nielsen number”, Pacific J. Math., 122:2 (1986), 459–473 | MR | Zbl

[3] Schirmer H., “Fixed point sets of deformations of pairs of spaces”, Topology Appl., 23 (1986), 193–205 | DOI | MR | Zbl

[4] Schirmer H., “A survey of relative Nielsen fixed point theory”, Contemp. Math., 152 (1993), 291–309 | MR | Zbl

[5] Shi Gen Hua (Shih Ken-Hua), “On the least number of fixed points and Nielsen numbers”, Acta Math. Sinica, 16:2 (1966), 223–232 | Zbl

[6] Zhao Xuezhi, “A relative Nielsen number for the complement”, Lect. Notes in Math., 1411, Springer-Verlag, Berlin–New York, 1989, 189–199

[7] Wilczyn'ski D., “Fixed point free equivariant homotopy classes”, Fund. Math., 123 (1984), 47–59 | MR

[8] Fadell E., Wong P., “On deforming $G$-maps to be fixed point free”, Pacific. J. Math., 132:2 (1988) | MR | Zbl

[9] Wong P., “On the location of fixed points of $G$-deformations”, Topology Appl., 39 (1991), 159–165 | DOI | MR | Zbl

[10] Wong P., “Equivariant Nielsen fixed point theory for $G$-maps”, Pacific J. Math., 150 (1991), 179–200 | MR | Zbl

[11] Wong P., “Equivariant Nielsen fixed point theory and periodic points”, Contemp. Math., 152 (1993), 341–350 | Zbl

[12] Wong P., “Equivariant Nielsen numbers”, Pacific. J. Math., 159:1 (1993), 153–175 | MR

[13] Jiang B., “Lectures on Nielsen fixed point theory”, Contemp. Math., 14 (1982) | Zbl

[14] Brown R. F., The Lefschetz Fixed Point Theorem, Scott, Foresman and Co., Glenview, Ill., 1971