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Cutting and Pasting Zp-Manifolds(1)

Published online by Cambridge University Press:  20 November 2018

Kenneth Prevot
Kenneth Prevot*
Affiliation:
Department of Mathematics University Of TennesseeKnoxville, Tennessee 37916, USA
*
Current Address: Bell Laboratories, Denver, Colorado 80234, USA.
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Abstract

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Let Mn and Nn be n-dimensional closed smooth oriented Zp-manifolds where p is an odd prime and Zp is the cyclic group of order p. This paper determines necessary and sufficient conditions under which Mn and Nn are equivalent under a special equivariant cut and past equivalence.

The only invariants are (a) the Euler characteristics of the Zp-manifolds, (b) the Euler characteristics of the fixed point manifolds in each fixed point dimesnion with specified normal representations, and (c) the oriented Zp-stratified cobordism class of the Zp-manifolds.

Keywords

57D6557D8557D90Euler characteristicZp-stratified cobordismnormal representationZp-equivariant cut and paste equivalence
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 25 , Issue 1 , 01 March 1982 , pp. 13 - 28
Copyright
Copyright © Canadian Mathematical Society 1982

Footnotes

(1)

This paper constitutes part of the author's Ph.D. thesis written at M.I.T. The author would like to thank F. P. Peterson and E. Y. Miller for many instructive conversations.

References

1. Bredon, G. C., Introduction to Compact Transformation Groups, Academic Press, New York, N.Y., 1972.Google Scholar
2. Conner, P. E. and Floyd, E. E., Differential Periodic Maps, Academic Press, New York, N.Y., 1964.Google Scholar
3. Conner, P. E. and Floyd, E. E., Maps of Odd Period, Annals of Math., 84 (1966), pp. 132-156.Google Scholar
4. Heithecker, J., Aquivariantes Kontrolliertes Schneiden und Kleben. Math. Ann., 217 (1975), pp. 17-28.Google Scholar
5. Herman, J. and Kreck, M., Cutting and Pasting of Involutions and Fiberings over the Circle within a Bordism Class, Math. Ann., 214 (1975), pp. 11-17.Google Scholar
6. Karras, U., Kreck, M., Neumann, W., and Ossa, E., Cutting and Pasting of Manifolds; SK-Groups, Publish or Perish, Boston, MA, 1973.Google Scholar
7. Kosniowski, C., Actions of finite abelian groups, Pitman, London, 1978.Google Scholar
8. Miller, E. Y.: Local Isomorphism of Riemannian, Hermitian, and Combinatorial Manifolds, Ph.D. Thesis, Harvard University, Cambridge, MA, 1973.Google Scholar
9. Neumann, W. D., Manifold Cutting and Pasting Groups, Topology, 14 (1975), pp. 237-244.Google Scholar
10. Prevot, K. J., Equivariant Cutting and Pasting of Manifolds, Ph.D. Thesis, M.I.T., Cambridge, MA, 1977.Google Scholar
11. Prevot, K. J., Modifications of Controllable Cutting and Pasting, to appear in Houston J. of Math. Google Scholar
12. Reinhart, B. L., Cobordism and the Euler number, Topology, 2 (1963), pp. 173-177.Google Scholar
13. Spanier, E. H., Algebraic Topology, McGraw-Hill, New York, N.Y., 1966.Google Scholar
14. Strong, R. E., Notes on Cobordism Theory, Princeton University Press, Princeton, N.J., 1968.Google Scholar
15. Strong, R. E., Tangential Cobordism, Math. Ann., 216 (1973), 181-196.Google Scholar
16. Wall, C. T. C., Surgery on Compact Manifolds, Academic Press, London, 1970.Google Scholar