https://neckpinch.com/authors/akio-kawauchi/New arXiv papers by Akio Kawauchi, from Neckpinch Tue, 10 Nov 2026 04:10:28 GMT https://neckpinch.com/papers/2103.16001/arxiv:2103.16001Tue, 30 Mar 2021 00:00:00 GMTAkio Kawauchi — The classical Poincaré conjecture that every homotopy 3-sphere is diffeomorphic to the 3-sphere is confirmed by Perelman in arXiv papers solving Thurston's program on geometrizations of 3-manifolds. A new confirmation of this conjecture is given by a method of 4D topology. For this proof, the spun torus-knot of every knot in every homotopy 3-sphere is observed to be a ribbon torus-knot in the 4-sphere, where Smooth 4D Poincaré Conjecture and Ribbonness of a sphere-link with (not necessarily meridian-based) free fundamental group are used. By examining a disk-chord system of a ribbon solid torus bounded by the spun torus-knot,it is proved that the knot belongs to a 3-ball in the homotopy 3-sphere. Then by Bing's result, it is confirmed that the homotopy 3-sphere is diffeomorphic to the 3-sphere.Geometrization3-manifolds4-manifolds