What is recorded here?
An equivariant-bordism construction, detection theorem, 256-fold periodicity and a homotopy gap exclude Kervaire-invariant-one elements in the higher indexed dimensions. Combined with Browder's earlier restriction, the associated framed-manifold dimensions are limited to 2, 6, 14, 30, 62 and possibly 126 in this work.
Source-linked catalogue note. A detailed explanatory guide has not yet been prepared for this entry.
Scientific scope
The result does not settle dimension126; that is a boundary of these sources, not a claim that the case remains open today. Existing low-dimensional constructions and Browder's dimensional restriction are inherited.
Read the original work
- On the non-existence of elements of Kervaire invariant one
- On the non-existence of elements of Kervaire invariant one
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People and systems
Michael A. Hill; Michael J. Hopkins; Douglas C. Ravenel
Source-listed authors for the exact contribution; experimental subjects are not autonomous scientific authors. Source support and predecessor work retain separate roles. Individual effort shares and unresolved identities are not inferred.
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English catalogue narrative
Hill, Hopkins and Ravenel: high-dimensional Kervaire-invariant-one nonexistence
An equivariant-bordism construction, detection theorem, 256-fold periodicity and a homotopy gap exclude Kervaire-invariant-one elements in the higher indexed dimensions. Combined with Browder's earlier restriction, the associated framed-manifold dimensions are limited to 2, 6, 14, 30, 62 and possibly 126 in this work.
Scientific scope
The result does not settle dimension126; that is a boundary of these sources, not a claim that the case remains open today. Existing low-dimensional constructions and Browder's dimensional restriction are inherited.
Reading status
This is a source-linked WRS catalogue note. A full explanatory guide and independent scientific reconstruction have not been completed for this entry. Read the identified original work for its complete narrative and arguments.
People and systems
Michael A. Hill; Michael J. Hopkins; Douglas C. Ravenel
Source-listed authors for the exact contribution; experimental subjects are not autonomous scientific authors. Source support and predecessor work retain separate roles. Individual effort shares and unresolved identities are not inferred.