Intersection Forms of Spin 4-Manifolds and the Pin(2)-Equivariant Mahowald Invariant
Abstract
In studying the "11/8-Conjecture" on the Geography Problem in 4-dimensional topology, Furuta proposed a question on the existence of Pin(2)-equivariant stable maps between certain representation spheres. In this paper, we present a complete solution to this problem by analyzing the Pin(2)-equivariant Mahowald invariants. As a geometric application of our result, we prove a "10/8+4"-Theorem. We prove our theorem by analyzing 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 -based Atiyah-Hirzebruch spectral sequence.
Keywords
Cite
@article{arxiv.1812.04052,
title = {Intersection Forms of Spin 4-Manifolds and the Pin(2)-Equivariant Mahowald Invariant},
author = {Michael J. Hopkins and Jianfeng Lin and XiaoLin Danny Shi and Zhouli Xu},
journal= {arXiv preprint arXiv:1812.04052},
year = {2019}
}
Comments
116 pages, 15 figures. Minor revisions. Comments welcome!