On the non-existence of elements of Kervaire invariant one

Details On the non-existence of elements of Kervaire invariant one On the non-existence of elements of Kervaire invariant one

2009-08-26

arxiv.org/abs/0908.3724v2

Mathematics

Algebraic Topology

Revised with a simplified main argument and two appendices on foundational material. 158 pages

Scientific paper

We show that Kervaire invariant one elements in the homotopy groups of
spheres exist only in dimensions at most 126. 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. With the exception of dimension 126 this
resolves a longstanding problem in algebraic topology.

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