Geodesic
Existence of multiplicative structures in the theories of cobordism with singularities
Izvestiya. Mathematics , Tome 9 (1975) no. 5, pp. 1007-1034.

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In this paper is presented a proof of the existence of a multiplication in the theories of cobordism with singularities. For theories of cobordism with singularities of one type we investigate the questions of commutativity and associativity. As a consequence of our proof of the theorem concerning multiplication in unitary cobordism with singularities, we obtain a new construction of an admissible multiplication in the theory of cobordism with coefficients in $Z_q$, and in the Conner–Floyd theory $W_*(\mathbf C,2)$. Bibliography: 14 titles. 
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O. K. Mironov. Existence of multiplicative structures in the theories of cobordism with singularities. Izvestiya. Mathematics , Tome 9 (1975) no. 5, pp. 1007-1034. http://geodesic.mathdoc.fr/item/IM2_1975_9_5_a4/

[1] Anderson P., “Cobordism classes of squares of orientable manifolds”, Ann. Math., Ser. 2, 83 (1966), 47–53 | DOI | MR | Zbl

[2] Araki S., Toda H., “Multiplicative structures in $\mod{q}$ cohomology theories, I, II”, Osaka J. Math., 2:1 (1965), 71–115 ; 3:1 (1966), 81–120 | MR | Zbl | MR | Zbl

[3] Baas N., On bordism theories of manifolds with singularities, Aarhus Universitet Preprint Ser., No 31, 1970/71 | MR

[4] Bukhshtaber V. M., “Proektory v unitarnykh kobordizmakh, svyazannye s $SU$-teoriei”, Uspekhi matem. nauk, XXVII:6 (1972), 231–232

[5] Kamata M., “On the differential $d_3^{p,0}$ of $U$-cobordism spectral sequence”, Osaka J. Math., 8 (1971), 233–241 | MR | Zbl

[6] Morava J., Unitary cobordism and extraordinary $K$-theories, Preprint | MR

[7] Rowlett R., “The cobordism of involutions on orientable manifolds”, Proc. Amer. Math. Soc., 40:1 (1973), 309–314 | DOI | MR | Zbl

[8] Rudyak Yu., “Stabilnaya $k$-teoriya i bordizmy s osobennostyami”, Dokl. AN SSSR, 216:6 (1974), 1222–1226

[9] Smith L., “On realizing complex bordism modules, I, II, III”, Amer. J. Math., 92:4 (1970), 793–856 ; 93:1 (1971), 226–263 ; 94:3 (1972), 875–890 | DOI | MR | DOI | MR | Zbl | DOI | MR | Zbl

[10] Sullivan D., “The hauptvermutung for manifolds”, Bull. Amer. Math. Soc., 73 (1971), 598–600 | DOI | MR

[11] Sullivan D., “Geometric periodicity and the invariants of manifolds”, Manifolds (Amsterdam 1970, Proc. Nuffic Summer School), Lecture Notes in Mathematics, 197, Springer, Berlin, 1971, 44–75 | MR

[12] Stong R., Zametki po teorii kobordizmov, Mir, M., 1973 | MR | Zbl

[13] Toda H., “On spectra realizing exterior parts of the Steenrod algebra”, Topology, 10:1 (1971), 53–65 | DOI | MR | Zbl

[14] Rudyak Yu., “Formalnye gruppy i bordizmy s osobennostyami”, Matem. Sb., 96:4 (1975), 523–542 | MR | Zbl