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Singularities and Higher Torsion in Symplectic Cobordism

Published online by Cambridge University Press:  20 November 2018

Boris I. Botvinnik  and
Stanley O. Kochman
Boris I. Botvinnik
Affiliation:
Department of Mathematics University of Oregon Eugene, Oregon 97403 U.S.A. e-mail: , [email protected]
Stanley O. Kochman
Affiliation:
Department of Mathematics and Statistics York University 4700 Keele Street North York, Ontario M3J IP3 e-mail: , [email protected]
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Abstract

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In this paper we construct higher two-torsion elements of all orders in the symplectic cobordism ring. We begin by constructing higher torsion elements in the symplectic cobordism ring with singularities using a geometric approach to the Adams- Novikov spectral sequence in terms of cobordism with singularities. Then we show how these elements determine particular elements of higher torsion in the symplectic cobordism ring.

Keywords

55N2255T1557R90
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 46 , Issue 3 , 01 June 1994 , pp. 485 - 516
Copyright
Copyright © Canadian Mathematical Society 1994

References

1. Alexander, J. C., Cobordism ofMassey products, Trans. Amer. Math. Soc. 166(1972), 197–214.Google Scholar
2. Botvinnik, B.I., Manifolds with singularities and the Adams-Novikov spectral sequence, Lecture Notes Series of the London Math. Soc. 170, Cambridge University Press, Cambridge, England, 1992.Google Scholar
3. Botvinnik, B. I. and Kochman, S. O., Adams spectral sequence and higher torsion in MSp*, to appear.Google Scholar
4. Gorbunov, V. and Ray, N., Orientations of Spin bundles and symplectic cobordism, Publ. of the RIMS, Kyoto Univ. 28(1992), 39–55.Google Scholar
5. Devinatz, E. S., Hopkins, M. J. and Smith, J. H., Nilpotence and stable homotopy theory, Ann. of Math. 128(1988), 207–242.Google Scholar
6. Kochman, S. O., The symplectic cobordism ring I, Mem. Amer. Math. Soc. No. 228(1980).Google Scholar
7. Kochman, S. O., The symplectic cobordism ring II, Mem: Amer. Math. Soc. No. 271(1982).Google Scholar
8. Kochman, S. O., The symplectic cobordism ring HI, Mem. Amer. Math. Soc. No. 496(1993).Google Scholar
9. Kochman, S. O., The ring structure of BoP%, Contemporary Math. 146(1993), 171–198.Google Scholar
10. May, J. P., Matrix Massey products,. Algebra 12(1969), 533–568.Google Scholar
11. Lashof, R., Poincaré duality and cobordism, Trans. Amer. Math. Soc. 109(1963), 257–277'.Google Scholar
12. Ravenel, D. C., Complex Cobordism and Stable Homotopy Groups, Academic Press, Orlando, Florida, 1986.Google Scholar
13. Ray, N., Indécomposables in Tors MSp*, Topology 10(1971), 261–270.Google Scholar
14. Segal, D., On the symplectic cobordism ring, Comment. Math. Helv. 45(1970), 159–169.Google Scholar
15. Toda, H., Composition methods in homotopy groups of spheres, Ann. of Math. Studies No. 49, Princeton Univ. Press, Princeton, N.J., 1962.Google Scholar
16. Vershinin, V. V., Computation of the symplectic cobordism ring below the dimension 32 and nontriviality of the majority of triple products of the Ray elements, Siberian Math. J. 24(1983), 41–51.Google Scholar
17. Vershinin, V. V., Symplectic cobordism with singularities, Izv. Akad. Nauk SSSR Ser. Mat. 24(1983), 230–247.Google Scholar
18. Vershinin, V. V., On bordism ring with principal torsion ideal, to appear.Google Scholar