The String bordism of $BE_8$ and $BE_8\times BE_8$ through dimension 14

TL;DR

This paper computes low-dimensional String bordism groups of $BE_8$ and $BE_8\times BE_8$ using spectral sequences and comparisons to Spin bordism, advancing understanding of their topological structures.

Contribution

It provides new calculations of String bordism groups for these classifying spaces, employing spectral sequences and comparative methods.

Findings

Computed String bordism groups up to dimension 14.

Established relationships between String and Spin bordism groups.

Enhanced methods for calculating bordism groups of classifying spaces.

Abstract

We compute the low dimensional String bordism groups of $BE_8$ and $BE_8\times BE_8$ using a combination of Adams spectral sequences together with comparisons to the Spin bordism cases.