Cappell-Shaneson homotopy spheres are standard

By S. Akbulut. 2009

64 citations recorded by the source corpus.

We show here that an infinite sequence of homotopy 4-spheres constructed by Cappell-Shaneson are all diffeomorphic to S 4 . This generalizes previous results of Akbulut-Kirby and Gompf.

Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/98371a374b5e50284fb789589f3665cb6547883f

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Discrete Mathematics and Combinatorics

In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Man and machine thinking about the smooth 4-dimensional Poincaré conjecture (2009, methodology): “The calculation was discontinued when Akbulut proved Bm = B4 for all m. Shortly thereafter, Nathan Dunfield contacted us with a better presentation of K3, see §4.2, which would probably make the calculation (indeed, of the full Khovanov homology, not just the s-invariant) feasible.”
Fibered knots and potential counterexamples to the Property 2R and Slice-Ribbon Conjectures (2010, methodology): “Akbulut’s recent proof [Ak] that infinitely many Cappell-Shaneson homotopy 4-spheres are standard again relies on such a trick.”
More Cappell–Shaneson spheres are standard (2009, background): “corresponding to all the matrices Am and twisted framing; the derivation by a long sequence of Kirby moves appeared in [G2]. These diagrams stood for two decades until a clever observation of Akbulut [A3] showed they were all diﬀeomorphic to the m= 0 case, and hence standard. The arguments trivializ”