Jianfeng Lin & Zhouli Xu (MIT)

The Pin(2)-Equivariant Mahowald Invariant

The existence of Pin(2)-equivariant stable maps between representation spheres has deep applications in 4-dimensional topology. We will sketch the proof for our main result on the Pin(2)-equivariant Mahowald invariants.

More specifically, we will discuss the Pin(2)-equivariant Mahowald invariants of powers of certain Euler classes in the RO(Pin(2))-graded equivariant stable homotopy groups of spheres. The proof analyzes maps between certain finite spectra arising from BPin(2) and various Thom spectra associated with it. To analyze these maps, we use the technique of cell-diagrams, known results on the stable homotopy groups of spheres, and the j-based Atiyah-Hirzebruch spectral sequence.

This is joint work with Mike Hopkins and XiaoLin Danny Shi. This talk provides the homotopy theory required by the first talk but will not depend upon it.