Vertex F-algebra structures on the complex oriented homology of H-spaces

TL;DR

This paper constructs graded vertex F-algebra structures on the complex-oriented homology of H-spaces, generalizing Joyce's vertex algebra using topological methods and formal group laws.

Contribution

It introduces a topological construction of graded vertex F-algebras on homology, extending Joyce's vertex algebra to complex-oriented homology theories.

Findings

Constructs graded vertex F-algebras on homology of H-spaces

Generalizes Joyce's vertex algebra to complex-oriented homology

Uses formal group laws associated with homology theories

Abstract

We give a topological construction of graded vertex F-algebras that generalizes Joyce's vertex algebra to complex-oriented homology. Given an H-space X with a BU(1)-action, a certain choice of K-theory class, and a complex oriented homology theory E, we build a graded vertex F-algebra structure on the homology $E_*(X)$ where F is the formal group law associated with E.