Symplectic Cobordism in Small Dimensions and a Series of Elements of Order Four

Abstract

We present the structure of symplectic cobordism ring $MSp_{*}$ in dimensions up to 51 and give a construction of an infinite series of elements $\Gamma_i$, $ i=1, 3,4, ...$, of order four in this ring, where $\operatorname{dim} \, \Gamma_i=8i+95$. The key element of the series is $\Gamma_1$ in dimension 103.