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On realization of Whitehead torsion

Published online by Cambridge University Press:  24 October 2008

Slawomir Kwasik
Slawomir Kwasik
Affiliation:
Department of Mathematics, Purdue University, West Lafayette, IN 47907, U.S.A.
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Abstract

We prove that the Poincaré conjecture implies that the 4-dimensional version of the realization theorem for Whitehead torsion is false. We show that infinitely many examples may be constructed to demonstrate this.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 98 , Issue 2 , September 1985 , pp. 271 - 273
Copyright
Copyright © Cambridge Philosophical Society 1985

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References

REFERENCES

[1]Cohen, M.. A Course in Simple-Homotopy Theory, Graduate Texts in Mathematics 10 (Springer- Verlag, 1973).CrossRefGoogle Scholar
[2]Hambleton, I. and Milgram, R. J.. The surgery obstruction groups for finite 2-groups. Invent. Math. 61 (1980), 33–52.CrossRefGoogle Scholar
[3]Milnor, J.. Whitehead torsion. Bull. Amer. Math. Soc. 72 (1966), 358–426.CrossRefGoogle Scholar
[4]Plotnick, S. P.. Vanishing of Whitehead groups for Seifert manifold with infinite fundamental group. Comment. Math. Helv. 55 (1980), 654–667.CrossRefGoogle Scholar
[5]Plotnick, S. P.. Homotopy equivalences and free modules. Topology 21 (1982), 91–99.CrossRefGoogle Scholar
[6]Oliver, R.. SK1 for finite group rings, III. In Algebraic K-Theory (Evanston 1980), Lecture Notes in Math. vol. 854 (Springer-Verlag, 1981), 299–337.Google Scholar
[7]Orlik, P.. Seifert Manifolds, Lecture Notes in Math. vol. 291 (Springer-Verlag, 1972).CrossRefGoogle Scholar
[8]Ritter, G.. Free actions of Z8 on S3. Trans Amer. Math. Soc. 181 (1973), 795–212.Google Scholar
[9]Rourke, C. P. and Sanderson, B. J.. Introduction to Piecewise-Linear Topology (Springer-Verlag, 1972).CrossRefGoogle Scholar
[10]Rubinstein, J. H.. Free actions of some finite groups on S3:I. Math. Ann. 240 (1979), no. 2, 165–175.CrossRefGoogle Scholar
[11]Waldhausen, F.. Algebraic K-theory of generalized free products. Ann. of Math. 108 (1978), 135–256.CrossRefGoogle Scholar
[12]Wall, C. T. C.. Norms of units in group rings. Proc. London Math. Soc. (3) 29 (1974), 593–632.CrossRefGoogle Scholar
[13]Wall, C. T. C.. Classification of hermitian forms, VI: Group rings. Ann. of Math. 103 (1976), 1–80.CrossRefGoogle Scholar