Smooth Homotopy 4-Sphere-Reference-Cited by-同舟云学术

Smooth Homotopy 4-Sphere

Published:2023-09-26 Issue: Volume:22 Page:690-701
ISSN:2224-2880
Container-title:WSEAS TRANSACTIONS ON MATHEMATICS
language:en
Short-container-title:

Author:

Kawauchi Akio¹

Affiliation:

1. Osaka Central Advanced Mathematical Institute, Osaka Metropolitan University, Sugimoto, Sumiyoshi-ku, Osaka 558-8585, JAPAN

Abstract

It is shown that every homotopy 4-disk with boundary 3-sphere is diffeomorphic to the 4-disk, so that every smooth homotopy 4-sphere is diffeomorphic to the 4-sphere. As a consequence, it is also shown that any (smoothly) embedded 3-sphere in the 4-sphere splits the 4-sphere into two components of 4-manifolds which are both diffeomorphic to the 4-ball. The argument used for the proof also shows that any two homotopic diffeomorphisms of the stable 4-sphere are smoothly isotopic if one diffeomorphism allows a local diffeomorphism change, so that they are smoothly concordant and piecewise-linearly isotopic.

Publisher

World Scientific and Engineering Academy and Society (WSEAS)

Subject

General Mathematics

Reference35 articles.

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