The Wecken property of the projective plane

Boju Jiang

Banach Center Publications (1999)

  • Volume: 49, Issue: 1, page 223-225
  • ISSN: 0137-6934

Abstract

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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.

How to cite

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Jiang, Boju. "The Wecken property of the projective plane." Banach Center Publications 49.1 (1999): 223-225. <http://eudml.org/doc/208962>.

@article{Jiang1999,
abstract = {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.},
author = {Jiang, Boju},
journal = {Banach Center Publications},
keywords = {fixed point; Nielsen number; projective plane; Wecken property},
language = {eng},
number = {1},
pages = {223-225},
title = {The Wecken property of the projective plane},
url = {http://eudml.org/doc/208962},
volume = {49},
year = {1999},
}

TY - JOUR
AU - Jiang, Boju
TI - The Wecken property of the projective plane
JO - Banach Center Publications
PY - 1999
VL - 49
IS - 1
SP - 223
EP - 225
AB - 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.
LA - eng
KW - fixed point; Nielsen number; projective plane; Wecken property
UR - http://eudml.org/doc/208962
ER -

References

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  1. [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. Zbl47.0528.01
  2. [B2] L. E. J. Brouwer, Aufzählung der Abbildungsklassen endlichfach zusammenhängender Flächen, Math. Ann. 82 (1921) 280-286. Zbl48.0649.01
  3. [Br] R. F. Brown, Nielsen fixed point theory on manifolds, these proceedings. 
  4. [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.. Zbl0861.55003
  5. [GH] M. J. Greenberg and J. R. Harper, Algebraic Topology, A First Course, Benjamin/Cummings, Reading, Massachusetts, 1981. Zbl0498.55001
  6. [Ha] B. Halpern, Periodic points on the Klein bottle, preprint, 1978. 
  7. [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. Zbl0845.55004
  8. [H1] H. Hopf, Über Mindestzahlen von Fixpunkten, Math. Z. 26 (1927) 762-774. Zbl53.0554.01
  9. [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. Zbl54.0611.02
  10. [J] B. Jiang, On the least number of fixed points, Amer. J. Math. 102 (1980) 749-763. Zbl0455.55001
  11. [O] P. Olum, Mappings of manifolds and the notion of degree, Ann. of Math. 58 (1953) 458-480. Zbl0052.19901

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