Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Wecken property for roots

Authors: Daciberg Gonçalves and Peter Wong
Journal: Proc. Amer. Math. Soc. 133 (2005), 2779-2782
MSC (2000): Primary 55M20, 55R20, 55T10; Secondary 55S35
Published electronically: March 22, 2005
MathSciNet review: 2146228
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We show that maps from a compact space into a topological manifold which have geometric Nielsen root number zero satisfy the Wecken property, i.e., $N(f;a)=0 \Rightarrow f\sim g$ such that $g^{-1}(a)=\emptyset$.

References [Enhancements On Off] (What's this?)

  • 1. R. Brooks, Certain subgroups of the fundamental group and the number of roots of $f(x)=a$, Amer. J. Math. 95 (1973), 720-728.MR 0346777 (49:11501)
  • 2. -, On the sharpness of the $\Delta_{2}$ and $\Delta_{1}$ Nielsen numbers, J. Reine Angew. Math. 259 (1973), 101-108.MR 0331373 (48:9706)
  • 3. M. Brown, A mapping theorem for untriangulated manifolds, in Topology of $3$-manifolds pp. 92-94, M.K. Fort, Jr. (editor), Prentice-Hall, Englewood Cliffs, New Jersey, 1962. MR 0158374 (28:1599)
  • 4. R. F. Brown and H. Schirmer, Nielsen root theory and Hopf degree theory, Pacific J. Math. 198 (2001), 49-80. MR 1831972 (2002c:55005)
  • 5. P. Doyle and J. Hocking, A decomposition theorem for $n$-dimensional manifolds, Proc. Amer. Math. Soc. 13 (1962), 469-471. MR 0141101 (25:4514)
  • 6. D. Gonçalves and C. Aniz, The minimizing of the Nielsen root classes, Central European J. Math. 2 (2004), 112-122. MR 2041673 (2004k:55004)
  • 7. D. Gonçalves and D. Randall, Self-coincidence of maps from $S^q$-bundles over $S^n$ to $S^n$, Boletin de la Sociedad Matematica Mexicana, to appear.
  • 8. H. Hopf, Zur Topologie der Abbildungen von Mannigfaltigkeiten, Zweiter Teil, Math. Ann., 102 (1930), 562-623.
  • 9. H. Schirmer, Mindestzahlen von Koinzidenzpunkten, J. Reine Angew. Math. 194 (1955), 21-39. MR 0073172 (17:394e)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 55M20, 55R20, 55T10, 55S35

Retrieve articles in all journals with MSC (2000): 55M20, 55R20, 55T10, 55S35

Additional Information

Daciberg Gonçalves
Affiliation: Department de Matemática - IME - USP, Caixa Postal 66.281, CEP 05311-970, São Paulo - SP, Brasil

Peter Wong
Affiliation: Department of Mathematics, Bates College, Lewiston, Maine 04240

Keywords: Nielsen number, Reidemeister number, Wecken property
Received by editor(s): October 7, 2003
Received by editor(s) in revised form: April 28, 2004
Published electronically: March 22, 2005
Additional Notes: This work was conducted during the first author’s visit to Bates College, April 11-23, 2003, and the second author’s visits to São Paulo, May 13-20, 2003 and April 27 - May 4, 2004. The first author’s visit was partially supported by the “Projeto temático Topologia Algébrica e Geométrica-FAPESP". The second author’s visits were partially supported by a grant from Bates College, the N.S.F., and the “Projeto temático Topologia Algébrica e Geométrica-FAPESP"
Communicated by: Paul Goerss
Article copyright: © Copyright 2005 American Mathematical Society

American Mathematical Society