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

TL;DR

This paper analyzes the structure of the symplectic cobordism ring in small dimensions and constructs an infinite series of elements of order four, revealing new algebraic structures in low-dimensional topology.

Contribution

It provides the detailed structure of the symplectic cobordism ring up to dimension 51 and introduces a novel infinite series of order four elements in this ring.

Findings

Structure of $MSp_{*}$ up to dimension 51 elucidated

Constructed an infinite series of elements $ ext{ extbackslash Gamma}_i$ of order four

Identified key element $ ext{ extbackslash Gamma}_1$ in dimension 103

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.