Let M be an n-dimensional, differential, compact and closed manifold and let c be a characteristic class of degree greater or equal to (n+1)/2. We will prove that if the class c anihilates all the characteristic numbers of M, where it enters as a factor, then the manifold M is cobordant to a manifold in which the class c is zero. Also, we will examine the case of manifolds with an extra structure.
KeywordsNumber Theory Algebraic Geometry Topological Group Characteristic Class Characteristic Number
Unable to display preview. Download preview PDF.
- 1.BROWDER, W. Surgery on simply connected manifolds. Berlin-Heidelberg-New York: Springer 1972Google Scholar
- 2.Hu, S. T. London-New York: Academic Press 1959Google Scholar
- 3.LASHOF, R. Poincaré duality and cobordism. Trans. Amer. Math. Soc. 109, 257–277 (1963)Google Scholar
- 4.McLANE, S. Homology. Berlin-Heidelberg-New York: Springer 1967Google Scholar
- 5.PAPASTAVRIDIS S. Killing characteristic classes by surgery. Proc, Amer. Math. Soc. 63, 353–358 (1977)Google Scholar
- 6.REED, T. Killing cohomology. classes by surgery. Proceedings of the Advanced Studies Institute on Algebraic Topology, August 1970. Aarthus University, Various Publications Series No. 13, p. 446–456Google Scholar
- 7.SPANIER, E. Algebraic Topology. New York-San Francisco-St. Louis-Toronto-London-Sidney: McGraw-Hill 1966Google Scholar
- 8.WALL, C. T. C. Surgery on Compact Manifolds. London-New York: Academic Press 1970Google Scholar