Singularities and Higher Torsion in Symplectic Cobordism
Canadian journal of mathematics, Tome 46 (1994) no. 3, pp. 485-516

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

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.
DOI : 10.4153/CJM-1994-026-7
Mots-clés : 55N22, 55T15, 57R90
Botvinnik, Boris I.; Kochman, Stanley O. Singularities and Higher Torsion in Symplectic Cobordism. Canadian journal of mathematics, Tome 46 (1994) no. 3, pp. 485-516. doi: 10.4153/CJM-1994-026-7
@article{10_4153_CJM_1994_026_7,
     author = {Botvinnik, Boris I. and Kochman, Stanley O.},
     title = {Singularities and {Higher} {Torsion} in {Symplectic} {Cobordism}},
     journal = {Canadian journal of mathematics},
     pages = {485--516},
     year = {1994},
     volume = {46},
     number = {3},
     doi = {10.4153/CJM-1994-026-7},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1994-026-7/}
}
TY  - JOUR
AU  - Botvinnik, Boris I.
AU  - Kochman, Stanley O.
TI  - Singularities and Higher Torsion in Symplectic Cobordism
JO  - Canadian journal of mathematics
PY  - 1994
SP  - 485
EP  - 516
VL  - 46
IS  - 3
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CJM-1994-026-7/
DO  - 10.4153/CJM-1994-026-7
ID  - 10_4153_CJM_1994_026_7
ER  - 
%0 Journal Article
%A Botvinnik, Boris I.
%A Kochman, Stanley O.
%T Singularities and Higher Torsion in Symplectic Cobordism
%J Canadian journal of mathematics
%D 1994
%P 485-516
%V 46
%N 3
%U http://geodesic.mathdoc.fr/articles/10.4153/CJM-1994-026-7/
%R 10.4153/CJM-1994-026-7
%F 10_4153_CJM_1994_026_7

[1] 1. Alexander, J. C., Cobordism ofMassey products, Trans. Amer. Math. Soc. 166(1972), 197–214. Google Scholar

[2] 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] 3. Botvinnik, B. I. and Kochman, S. O., Adams spectral sequence and higher torsion in MSp*, to appear. Google Scholar

[4] 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] 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] 6. Kochman, S. O., The symplectic cobordism ring I, Mem. Amer. Math. Soc. No. 228(1980). Google Scholar

[7] 7. Kochman, S. O., The symplectic cobordism ring II, Mem: Amer. Math. Soc. No. 271(1982). Google Scholar

[8] 8. Kochman, S. O., The symplectic cobordism ring HI, Mem. Amer. Math. Soc. No. 496(1993). Google Scholar

[9] 9. Kochman, S. O., The ring structure of BoP%, Contemporary Math. 146(1993), 171–198. Google Scholar

[10] 10. May, J. P., Matrix Massey products,. Algebra 12(1969), 533–568. Google Scholar

[11] 11. Lashof, R., Poincaré duality and cobordism, Trans. Amer. Math. Soc. 109(1963), 257–277'. Google Scholar

[12] 12. Ravenel, D. C., Complex Cobordism and Stable Homotopy Groups, Academic Press, Orlando, Florida, 1986. Google Scholar

[13] 13. Ray, N., Indécomposables in Tors MSp*, Topology 10(1971), 261–270. Google Scholar

[14] 14. Segal, D., On the symplectic cobordism ring, Comment. Math. Helv. 45(1970), 159–169. Google Scholar

[15] 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] 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] 17. Vershinin, V. V., Symplectic cobordism with singularities, Izv. Akad. Nauk SSSR Ser. Mat. 24(1983), 230–247. Google Scholar

[18] 18. Vershinin, V. V., On bordism ring with principal torsion ideal, to appear. Google Scholar

Cité par Sources :