English

Detecting exotic spheres in low dimensions using coker J

Algebraic Topology 2020-02-12 v4

Abstract

Building off of the work of Kervaire and Milnor, and Hill, Hopkins, and Ravenel, Xu and Wang showed that the only odd dimensions n for which S^n has a unique differentiable structure are 1, 3, 5, and 61. We show that the only even dimensions below 140 for which S^n has a unique differentiable structure are 2, 6, 12, 56, and perhaps 4.

Cite

@article{arxiv.1708.06854,
  title  = {Detecting exotic spheres in low dimensions using coker J},
  author = {Mark Behrens and Michael Hill and Michael J. Hopkins and Mark Mahowald},
  journal= {arXiv preprint arXiv:1708.06854},
  year   = {2020}
}

Comments

52 pages. Revised version includes some additional recommendations of referee

R2 v1 2026-06-22T21:21:15.273Z