Disproves the Smale Conjecture for S^4 by showing Diff(S^4) is not SO(5).
problem Disproving the Smale Conjecture for S^4.
method Directly showing π₀Diff(S^4) ≠ 0 by proving a loose-cork cannot be a loose-cork.
result Diff(S^4) ≠ SO(5).
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Homotopy 4-spheres created by iterated Gluck twists of S^4.
problem Understanding the creation and properties of homotopy 4-spheres.
method Using iterated Gluck twists and handle cancellations to show homotopy equivalence to S^4.
result Homotopy spheres Σ_n formed by doubling an infinite order loose-cork are homotopy equivalent to S^4.
On a homotopy -spheremath.GT
Standard proved to be diffeomorphic to a curious homotopy sphere.
problem Determining the diffeomorphism of a curious homotopy sphere to the standard .
method Proof based on properties of homotopy spheres and loose corks.
result The curious homotopy sphere is diffeomorphic to the standard .
Concrete description of infinite order cork automorphism.
problem Describing the infinite order loose-cork automorphism.
method Concatenating the defining ribbon disk by an infinite order isotopy.
result Concrete description of the infinite order cork automorphism.
On infinite order corksmath.GT
We construct an infinite order loose cork.
Study of contractible manifolds and their twists to determine if they are .
problem Determine if a specific manifold is using twists and handlebody descriptions.
method Analyze two contractible manifolds, one Stein and one non-Stein, with non-trivial boundary mapping classes. Use a specific homotopy sphere to test if it is .
result Show that a specific manifold is indeed .