Annals of Mathematics· 2016Q1
On the nonexistence of elements of Kervaire invariant one
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- 2016year
Short summary
Kervaire invariant one elements θj exist only for j ≤ 6, meaning smooth framed manifolds with Kervaire invariant one only exist in dimensions 2, 6, 14, 30, 62, and possibly 126.
AI-generated from the title and abstract; the full text is not read.
Key points
- Kervaire invariant one elements θj are shown to exist only for j ≤ 6.
- This implies smooth framed manifolds of Kervaire invariant one exist only in dimensions 2, 6, 14, 30, 62, and possibly 126.
- The result resolves a longstanding problem in algebraic topology, except for the dimension 126 case.
AI-generated from the title and abstract; the full text is not read.
Abstract
We show that the Kervaire invariant one elements θj ∈ π2j+1−2S exist only for j ≤ 6. By Browder’s Theorem, this means that smooth framed manifolds of Kervaire invariant one exist only in dimensions 2, 6, 14, 30, 62, and possibly 126. Except for dimension 126 this resolves a longstanding problem in algebraic topology.
The authors' abstract, as published at the source. Annals of Mathematics, 2016 · DOI ↗
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Field: Mathematical Physics
Mathematical PhysicsMathematics