Geodesic
On the decomposition of certain spectra
Sbornik. Mathematics, Tome 60 (1988) no. 2, pp. 283-290 
V. V. Vershinin. On the decomposition of certain spectra. Sbornik. Mathematics, Tome 60 (1988) no. 2, pp. 283-290. http://geodesic.mathdoc.fr/item/SM_1988_60_2_a0/
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     title = {On~the~decomposition of~certain spectra},
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Voir la notice de l'article provenant de la source Math-Net.Ru

Decompositions of spectra corresponding to cobordism theories with singularities are examined, and also relations between the Adams and Adams–Novikov spectral sequences and spectral sequences of singularities. A multiplicative variant of the indecomposable spectrum $BoP$ is constructed, this being a direct summand in the splitting of the spectrum $MSU$ of special unitary cobordism theory. Bibliography: 14 titles.

[1] Adams J. F., “Lectures on generalised cohomology”, Lecture Notes in Mathematics, 99, Berlin a. o., 1969, 1–138 | MR

[2] Tom R., “Nekotorye svoistva “v tselom” differentsiruemykh mnogoobrazii”, Rassloennye prostranstva i ikh prilozhenie, M., 1958, 293–351

[3] Novikov S. P., “O nekotorykh zadachakh topologii mnogoobrazii, svyazannykh s teoriei prostranstv Toma”, DAN SSSR, 132:5 (1960), 1031–1034 | Zbl

[4] Novikov S. P., “Gomotopicheskie svoistva kompleksov Toma”, Matem. sb., 57(99) (1962), 406–442 | MR

[5] Brown E. H., Peterson F. P., “A spectrum whose $Z_p$ cohomology is the algebra of reduced $p^{\text{th}}$ powers”, Topology, 5:2 (1966), 149–154 | DOI | MR | Zbl

[6] Quillen D., “On the formal group laws of unoriented and complex cobordism theory”, Bull. Amer. Math. Soc., 75:6 (1969), 1293–1298 | DOI | MR | Zbl

[7] Pengelley D. J., “The homotopy type of MSU”, Amer. J. Math., 104:5 (1982), 1101–1123 | DOI | MR | Zbl

[8] Novikov S. P., “Metody algebraicheskoi topologii s tochki zreniya teorii kobordizmov”, Izv. AN SSSR. Ser. matem., 31:4 (1967), 855–951 | Zbl

[9] Baas N.-A., “On bordism theory of manifolds with singularities”, Math. Scand., 33:2 (1973), 279–302 | MR

[10] Vershinin V. V., “Simplekticheskie kobordizmy s osobennostyami”, Izv. AN SSSR. Ser. matem., 47:2 (1983), 230–247 | MR | Zbl

[11] Botvinnik B. I., Algebraicheskie i geometricheskie svoistva spektralnoi posledovatelnosti Adamsa–Novikova, Dis. $\dots$ kand. fiz.-matem. nauk NGU, Novosibirsk, 1983

[12] Vershinin V. V., “Algebraicheskaya spektralnaya posledovatelnost S. P. Novikova dlya spektra $MSp$”, Sib. matem. zhurn., 21:1 (1980), 26–43 | MR | Zbl

[13] Ray N., “Indecomposable in Tors $MSp^*$”, Topology, 10:4 (1971), 261–270 | DOI | MR | Zbl

[14] Mironov O. K., “Suschestvovanie multiplikativnykh struktur v teoriyakh kobordizmov s osobennostyami”, Izv. AN SSSR. Ser. matem., 39:5 (1975), 1065–1092 | MR | Zbl