Line Bundle Twists for Unitary Bordism are Ghosts

Abstract

We prove that the canonical twist $\zeta :K(\mathbb{Z},3)\to BG{L}_1(MSpi{n}^c)$ does not extend to a twist for unitary bordism by showing that every continuous map $f:K(\mathbb{Z},3)\to BG{L}_1(MU)$ loops to a null homotopic map.

arXiv comment12 pages, comments are welcome!

References in corpus (4)

• An $\infty$-categorical approach to $R$-line bundles, $R$-module Thom spectra, and twisted $R$-homology
• Units of ring spectra, orientations, and Thom spectra via rigid infinite loop space theory
• Twisted Spin cobordism and positive scalar curvature
• Homotopical and operator algebraic twisted K-theory