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)



On mapping cones of suspension elements of finite order in the homotopy groups of a wedge of spheres

Author: Imre Bokor
Journal: Proc. Amer. Math. Soc. 119 (1993), 955-961
MSC: Primary 55P15
MathSciNet review: 1152974
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: The genus of the mapping cone $ {C_f}$ of a map $ f:{S^{m - 1}} \to \bigvee{S^n}(m > n > 1)$ representing a suspension element of finite order in $ {\pi _{m - 1}}(\bigvee{S^n})$ is classified by a subgroup $ {G_f}$ of $ {\pi _{m - 1}}({S^n})$ depending only on the homotopy type of $ {C_f}$. The group $ {G_f}$ finds application in proving that the genus of $ {C_f}$ is trivial whenever $ {C_f}$ has sufficiently many $ n$-cells, the number being limited by the torsion subgroup of $ {\pi _{m - 1}}({S^n})$.

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

  • [1] Imre Bokor, On genus and cancellation in homotopy, Israel J. Math. 73 (1991), no. 3, 361–379. MR 1135224, 10.1007/BF02773848
  • [2] Peter Hilton, Guido Mislin, and Joe Roitberg, Localization of nilpotent groups and spaces, North-Holland Publishing Co., Amsterdam-Oxford; American Elsevier Publishing Co., Inc., New York, 1975. North-Holland Mathematics Studies, No. 15; Notas de Matemática, No. 55. [Notes on Mathematics, No. 55]. MR 0478146
  • [3] I. Llerena, Wedge cancellation and genus (submitted).
  • [4] Irene Llerena, Wedge cancellation of certain mapping cones, Compositio Math. 81 (1992), no. 1, 1–17. MR 1145605
  • [5] John Milnor, On simply connected 4-manifolds, Symposium internacional de topología algebraica International symposi um on algebraic topology, Universidad Nacional Autónoma de México and UNESCO, Mexico City, 1958, pp. 122–128. MR 0103472
  • [6] Edward A. Molnar, Relation between wedge cancellation and localization for complexes with two cells, J. Pure Appl. Algebra 3 (1973), 141–158. MR 0317323
  • [7] Clarence Wilkerson, Genus and cancellation, Topology 14 (1975), 29–36. MR 0367995

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 55P15

Retrieve articles in all journals with MSC: 55P15

Additional Information

Keywords: CW complex, genus, suspension
Article copyright: © Copyright 1993 American Mathematical Society