A proof is given of the fact that the real projective plane $P^2$ has the Wecken property, i.e. for every selfmap $f:P^2 → P^2$, the minimum number of fixed points among all selfmaps homotopic to f is equal to the Nielsen number N(f) of f.
Department of Mathematics, Peking University, Beijing 100871, China
Bibliografia
[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.
[B2] L. E. J. Brouwer, Aufzählung der Abbildungsklassen endlichfach zusammenhängender Flächen, Math. Ann. 82 (1921) 280-286.
[Br] R. F. Brown, Nielsen fixed point theory on manifolds, these proceedings.
[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..
[GH] M. J. Greenberg and J. R. Harper, Algebraic Topology, A First Course, Benjamin/Cummings, Reading, Massachusetts, 1981.
[Ha] B. Halpern, Periodic points on the Klein bottle, preprint, 1978.
[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.
[H1] H. Hopf, Über Mindestzahlen von Fixpunkten, Math. Z. 26 (1927) 762-774.
[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.
[J] B. Jiang, On the least number of fixed points, Amer. J. Math. 102 (1980) 749-763.
[O] P. Olum, Mappings of manifolds and the notion of degree, Ann. of Math. 58 (1953) 458-480.