The Wecken property of the projective plane
Jiang, Boju
Banach Center Publications, Tome 50 (1999), p. 223-225 / Harvested from The Polish Digital Mathematics Library

A proof is given of the fact that the real projective plane P2 has the Wecken property, i.e. for every selfmap f:P2P2, the minimum number of fixed points among all selfmaps homotopic to f is equal to the Nielsen number N(f) of f.

Publié le : 1999-01-01
EUDML-ID : urn:eudml:doc:208962
@article{bwmeta1.element.bwnjournal-article-bcpv49i1p223bwm,
     author = {Jiang, Boju},
     title = {The Wecken property of the projective plane},
     journal = {Banach Center Publications},
     volume = {50},
     year = {1999},
     pages = {223-225},
     zbl = {0938.55004},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-bcpv49i1p223bwm}
}
Jiang, Boju. The Wecken property of the projective plane. Banach Center Publications, Tome 50 (1999) pp. 223-225. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-bcpv49i1p223bwm/

[000] [B1] L. E. J. Brouwer, Über die Minimalzahl der Fixpunkte bei den Klassen von eindeutigen stetigen Transformationen der Ringflächen, Math. Ann. 82 (1921) 94-96. | Zbl 47.0528.01

[001] [B2] L. E. J. Brouwer, Aufzählung der Abbildungsklassen endlichfach zusammenhängender Flächen, Math. Ann. 82 (1921) 280-286. | Zbl 48.0649.01

[002] [Br] R. F. Brown, Nielsen fixed point theory on manifolds, these proceedings.

[003] [DHT] O. Davey, E. Hart and K. Trapp, Computation of Nielsen numbers for maps of closed surfaces, Trans. Amer. Math. Soc. 348 (1996) 3245-3266.. | Zbl 0861.55003

[004] [GH] M. J. Greenberg and J. R. Harper, Algebraic Topology, A First Course, Benjamin/Cummings, Reading, Massachusetts, 1981. | Zbl 0498.55001

[005] [Ha] B. Halpern, Periodic points on the Klein bottle, preprint, 1978.

[006] [HKW] P. Heath, E. Keppelmann and P. Wong, Addition formulae for Nielsen numbers and for Nielsen type numbers of fiber preserving maps, Topology Appl. 67 (1995) 133-157. | Zbl 0845.55004

[007] [H1] H. Hopf, Über Mindestzahlen von Fixpunkten, Math. Z. 26 (1927) 762-774. | Zbl 53.0554.01

[008] [H2] H. Hopf, Zur Topologie der Abbildungen von Mannigfaltigkeiten. I, Neue Darstellung der Theorie des Abbildungsgrades für topologische Mannigfaltigkeiten, Math. Ann. 100 (1928) 579-608; II, Klasseninvarianten von Abbildungen, Math. Ann. 102 (1929) 562-623. | Zbl 54.0611.02

[009] [J] B. Jiang, On the least number of fixed points, Amer. J. Math. 102 (1980) 749-763. | Zbl 0455.55001

[010] [O] P. Olum, Mappings of manifolds and the notion of degree, Ann. of Math. 58 (1953) 458-480. | Zbl 0052.19901