Hostname: page-component-cd9895bd7-q99xh Total loading time: 0 Render date: 2024-12-26T06:02:55.901Z Has data issue: false hasContentIssue false
  • English
  • Français

Some generalizations of the Borsuk–Ulam theorem and applications to realizing homotopy classes by embedded spheres

Published online by Cambridge University Press:  24 October 2008

Roger Fenn
Roger Fenn
Affiliation:
Istituto Matematico, Pisa University of Sussex
Get access Rights & Permissions [Opens in a new window]

Extract

In this paper, some theorems of the Borsuk-Ulam type (1) are given. One of these can be applied to show that certain homotopy classes in manifolds cannot be realized by embedded spheres. The n-dimensional sphere Sn is the subset of the euclidean space

Rn+l consisting of all points (x1, …,xn+1) satisfying . Let be a piecewise linear (PL) involution on Sn without fixed points.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 74 , Issue 2 , September 1973 , pp. 251 - 256
Copyright
Copyright © Cambridge Philosophical Society 1973

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

(1)Borsuk, K.Drei Satz uber die n-dimensionale Euklidische Sphare. Fund. Math. 20 (1933), 177–190.CrossRefGoogle Scholar
(2)Fenn, R.On Dehn's Lemma in 4 dimensions. Bull. London Math. Soc. 3 (1971), 79–81.CrossRefGoogle Scholar
(3)Kervaire, M. A. and Milnor, J. W.On 2-spheres in 4-manifolds. Proc. Nat. Acad. Sci. U.S.A. 47 (1961), 1651–1657.CrossRefGoogle ScholarPubMed
(4)Kervaire, M. A.Geometric and Algebraic intersection numbers. Comment. Math. Helv. 39, (1965), 271–280.CrossRefGoogle Scholar
(5)Wall, C. T. C.Surgery of non simply-connected manifolds. Ann. of Math. 84 (1966), 217–276.CrossRefGoogle Scholar
(6)Wall, C. T. C.Surgery on Compact Manifolds. London Mathematical Society Monographs No. 1 Academic Press.CrossRefGoogle Scholar
(7)Yang, Chung-Tao. On theorems of Bonuk-Ulam, Kakutani-Yamabe-Yujobo and Dyson, I. Ann. of Math. 60 (1954), 262–282.CrossRefGoogle Scholar
(8)Zeeman, E. C.Seminar on Combinatorial Topology. Institute des Hautes Etudes Scientifiques, vols. 1 and 8.Google Scholar