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 Γi, i = 1, 3,4, , . . . , of order four in this ring, where dim Γi = 8i + 95. The key element of the series is Γ1 in dimension 103.