Cutting and Pasting Zp-Manifolds(1)
Canadian mathematical bulletin, Tome 25 (1982) no. 1, pp. 13-28

Voir la notice de l'article provenant de la source Cambridge University Press

Let M n and N n be n-dimensional closed smooth oriented Z p-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 M n and N n 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.
DOI : 10.4153/CMB-1982-002-x
Mots-clés : 57D65, 57D85, 57D90, Euler characteristic, Zp-stratified cobordism, normal representation, Zp-equivariant cut and paste equivalence
Prevot, Kenneth. Cutting and Pasting Zp-Manifolds(1). Canadian mathematical bulletin, Tome 25 (1982) no. 1, pp. 13-28. doi: 10.4153/CMB-1982-002-x
@article{10_4153_CMB_1982_002_x,
     author = {Prevot, Kenneth},
     title = {Cutting and {Pasting} {Zp-Manifolds(1)}},
     journal = {Canadian mathematical bulletin},
     pages = {13--28},
     year = {1982},
     volume = {25},
     number = {1},
     doi = {10.4153/CMB-1982-002-x},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1982-002-x/}
}
TY  - JOUR
AU  - Prevot, Kenneth
TI  - Cutting and Pasting Zp-Manifolds(1)
JO  - Canadian mathematical bulletin
PY  - 1982
SP  - 13
EP  - 28
VL  - 25
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-1982-002-x/
DO  - 10.4153/CMB-1982-002-x
ID  - 10_4153_CMB_1982_002_x
ER  - 
%0 Journal Article
%A Prevot, Kenneth
%T Cutting and Pasting Zp-Manifolds(1)
%J Canadian mathematical bulletin
%D 1982
%P 13-28
%V 25
%N 1
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-1982-002-x/
%R 10.4153/CMB-1982-002-x
%F 10_4153_CMB_1982_002_x

[1] 1. Bredon, G. C., Introduction to Compact Transformation Groups, Academic Press, New York, N.Y., 1972. Google Scholar

[2] 2. Conner, P. E. and Floyd, E. E., Differential Periodic Maps, Academic Press, New York, N.Y., 1964. Google Scholar

[3] 3. Conner, P. E. and Floyd, E. E., Maps of Odd Period, Annals of Math., 84 (1966), pp. 132-156. Google Scholar

[4] 4. Heithecker, J., Aquivariantes Kontrolliertes Schneiden und Kleben. Math. Ann., 217 (1975), pp. 17-28. Google Scholar

[5] 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] 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] 7. Kosniowski, C., Actions of finite abelian groups, Pitman, London, 1978. Google Scholar

[8] 8. Miller, E. Y.: Local Isomorphism of Riemannian, Hermitian, and Combinatorial Manifolds, Ph.D. Thesis, Harvard University, Cambridge, MA, 1973. Google Scholar

[9] 9. Neumann, W. D., Manifold Cutting and Pasting Groups, Topology, 14 (1975), pp. 237-244. Google Scholar

[10] 10. Prevot, K. J., Equivariant Cutting and Pasting of Manifolds, Ph.D. Thesis, M.I.T., Cambridge, MA, 1977. Google Scholar

[11] 11. Prevot, K. J., Modifications of Controllable Cutting and Pasting, to appear in Houston J. of Math. Google Scholar

[12] 12. Reinhart, B. L., Cobordism and the Euler number, Topology, 2 (1963), pp. 173-177. Google Scholar

[13] 13. Spanier, E. H., Algebraic Topology, McGraw-Hill, New York, N.Y., 1966. Google Scholar

[14] 14. Strong, R. E., Notes on Cobordism Theory, Princeton University Press, Princeton, N.J., 1968. Google Scholar

[15] 15. Strong, R. E., Tangential Cobordism, Math. Ann., 216 (1973), 181-196. Google Scholar

[16] 16. Wall, C. T. C., Surgery on Compact Manifolds, Academic Press, London, 1970. Google Scholar

Cité par Sources :