Abstract:
It is proved that there exist multiplicative structures in the symplectic bordism theories with singularities of types $\Sigma_n$ and $\Sigma$, where
$\Sigma_n=(\theta_1,\Phi_1,\Phi_2,\Phi_4,\dots,\Phi_{2^{n-2}})$ and $\Sigma=(\theta_1,\Phi_1,\Phi_2,\Phi_4,\dots,\Phi_{2^j},\dots)$, and that the ring $MSp^\Sigma_*$ is isomorphic to a polynomial ring
$Z[w_1,\dots,w_i,\dots,x_2,x_4,\dots,x_k,\dots]$, where $i=1,2,3,\dots$; $k=2,4,5,\dots$, $k\ne2^j-1$; $\deg w_i=2(2^i-1)$ and $\deg x_k=4k$.
Bibliography: 10 titles.
This publication is cited in the following 5 articles:
Aleksandr L. Anisimov, Vladimir V. Vershinin, “Symplectic cobordism in small dimensions and a series of elements of order four”, J. Homotopy Relat. Struct, 2012
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
Nigel Ray, “On a construction in bordism theory”, Proc Edin Math Soc, 29:3 (1986), 413