Detecting exotic spheres in low dimensions using coker J

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.

arXiv comment52 pages. Revised version includes some additional recommendations of referee

References in corpus (9)

• Ricci flow with surgery on three-manifolds
• Finite extinction time for the solutions to the Ricci flow on certain three-manifolds
• On the homotopy of Q(3) and Q(5) at the prime 2
• Classical and motivic Adams charts
• A modular description of the K(2)-local sphere at the prime 3
• On the ring of cooperations for 2-primary connective topological modular forms
• Connective versions of TMF(3)
• The homotopy groups of the spectrum Tmf
• The special fiber of the motivic deformation of the stable homotopy category is algebraic

Cited by in corpus (6)

• Stable homotopy groups of spheres
• Connected sum decompositions of high-dimensional manifolds
• The 2-primary Hurewicz image of tmf
• (Topological) modular forms with level structures: decompositions and duality
• A survey of the homology cobordism group
• Connective Models for Topological Modular Forms of Level $n$