Abstract
A theorem on the existence of the unique minimal topologic handle decomposition of differentiable simply connected five-dimensional manifolds is proved. For a decomposition of this sort, the number of handles of each index is given.
References
R. Kirby and L. Sibenman, “Foundational essay on topological manifolds, smoothing and triangulations,”Ann. Math. Stud.,88 (1977).
S. Smale, “Generalized Poincaré's conjecture in dimensions greater than four,”Ann. Math.,74, No. 2, 391–406 (1961).
D. Barden, “Simply connected five-manifolds,”Ann. Math.,82, 365–385 (1965).
Yu. A. Shkol'nikov, “Handle decomposition of simply connected five-manifolds. III,”Ukr. Mat. Zh.,46, No. 7, 935–940 (1994).
V. V. Sharko,Functions on Manifolds [in Russian], Naukova Dumka, Kiev (1990).
C. P. Rourke and B. J. Sanderson,Introduction to Piecewise-Linear Topology, Springer, Berlin (1972).
J. Milnor,Lectures on the h-Cobordism Theorem, Princeton University Press, Princeton (1965).
M. Freedman, “The topology of four-dimensional manifolds,”J. Different. Geom.,17, 357–453 (1982).
Author information
Authors and Affiliations
Additional information
Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 46, No. 12, pp. 1714–1720, December, 1994.
This research was partially supported by the International Scientific Foundation, grant No. V6F000.
Rights and permissions
About this article
Cite this article
Prishlyak, A.O. Minimal handle decomposition of smooth simply connected five-dimensional manifolds. Ukr Math J 46, 1907–1913 (1994). https://doi.org/10.1007/BF01063175
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01063175