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

Jacob Gross,Markus Upmeier

doi:10.1016/j.jpaa.2022.107019

Abstract

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

Highlights

Let E∗ be a complex oriented generalized cohomology theory with associated formal group law F (z, w) over its coefficient ring R∗, see §3
We present a Laurent-polynomial version of the Conner-Floyd Chern classes with values in E∗
Our result applies to the topological realization X = MtAop of a moduli stack

Summary

Introduction

Let E∗ be a complex oriented generalized cohomology theory with associated formal group law F (z, w) over its coefficient ring R∗, see §3. (c) (Normalization.) For a complex line bundle L → X and a ∈ E∗(X) we have a ∩ CzE (L) = a ∩ F (z, cE1 (L)). (i) The additive formal group law Ga over Z (in degree zero) is defined by F (z, w) = z + w, and the inverse is ι(z) = −z.

Results

Conclusion