Detecting exotic spheres in low dimensions using coker J

2017/08/31 by Mark Behrens, Michael Hill, Michael A. Hill +2 · 1 citation
Chemistry · Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Chemistry #Coker unit #Differentiable function #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Law #Mathematics #Organic chemistry #Physics #Political science #Pure mathematics #SPHERES #Separate spheres #Thermodynamics #Work (physics) #math.AT

paper · pdf · doi:10.1112/jlms.12301

52 pages. Revised version includes some additional recommendations of referee

arxiv created 2019/11/02 · openalex publication_date 2020/02/03 · arxiv updated 2020/02/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

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 Sⁿ has a unique differentiable structure are 1, 3, 5, and 61. We show that the only even dimensions below 140 for which Sⁿ has a unique differentiable structure are 2, 6, 12, 56, and perhaps 4.

Citations

• Classical and motivic Adams charts
• On the nonexistence of elements of Kervaire invariant one
• The Kervaire Invariant of Framed Manifolds and its Generalization
• On the groups J(X)—IV
• A new infinite family in 2π∗S
• Connective versions of TMF(3)
• On the formal group laws of unoriented and complex cobordism theory
• Finite extinction time for the solutions to the Ricci flow on certain three-manifolds
• Ricci flow with surgery on three-manifolds
• The homotopy groups of the spectrum Tmf
• The special fiber of the motivic deformation of the stable homotopy category is algebraic
• A modular description of the K(2)-local sphere at the prime 3
• The triviality of the 61-stem in the stable homotopy groups of spheres
• Stable Stems

Cited by

• Exotic sphere [wikipedia]

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