Abstract:
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 Zq, and in the Conner–Floyd theory W∗(C,2).
Bibliography: 14 titles.
Citation:
O. K. Mironov, “Existence of multiplicative structures in the theories of cobordism with singularities”, Math. USSR-Izv., 9:5 (1975), 1007–1034
\Bibitem{Mir75}
\by O.~K.~Mironov
\paper Existence of multiplicative structures in the theories of cobordism with singularities
\jour Math. USSR-Izv.
\yr 1975
\vol 9
\issue 5
\pages 1007--1034
\mathnet{http://mi.mathnet.ru/eng/im2080}
\crossref{https://doi.org/10.1070/IM1975v009n05ABEH001506}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=402784}
\zmath{https://zbmath.org/?q=an:0349.57013}
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https://www.mathnet.ru/eng/im2080
https://doi.org/10.1070/IM1975v009n05ABEH001506
https://www.mathnet.ru/eng/im/v39/i5/p1065
This publication is cited in the following 8 articles:
Semyon A. Abramyan, “Homology of the $MSU$ Spectrum”, Proc. Steklov Inst. Math., 318 (2022), 1–12
I. Yu. Limonchenko, T. E. Panov, G. S. Chernykh, “$SU$-bordism: structure results and geometric representatives”, Russian Math. Surveys, 74:3 (2019), 461–524
Vladimir V. Vershinin, Lecture Notes in Mathematics, 1474, Algebraic Topology Poznań 1989, 1991, 295
B. I. Botvinnik, “The structure of the ring $MSU_*$”, Math. USSR-Sb., 69:2 (1991), 581–596
V. V. Vershinin, “On the decomposition of certain spectra”, Math. USSR-Sb., 60:2 (1988), 283–290
V. V. Vershinin, “Symplectic cobordism with singularities”, Math. USSR-Izv., 22:2 (1984), 211–226
O. K. Mironov, “Steenrod–Dieck operations and obstructions for admissible multiplications in cobordism theories with singularities”, Russian Math. Surveys, 35:3 (1980), 260–263
O. K. Mironov, “Multiplications in cobordism theories with singularities, and Steenrod–tom Dieck operations”, Math. USSR-Izv., 13:1 (1979), 89–106
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