Symplectic cobordism with singularities

V. V. Vershinin

Izvestiya. Mathematics , Tome 22 (1984) no. 2, pp. 211-226

Résumé

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.