光滑同伦4球

Q3 Mathematics

WSEAS Transactions on Mathematics Pub Date : 2023-09-26 DOI:10.37394/23206.2023.22.76

Akio Kawauchi

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引用次数: 3

摘要

证明了每一个边界为3球的同伦4-盘都与4-盘是微同态的，因此每一个光滑同伦4-球都与4-球是微同态的。结果还表明，在4球中任意(平滑)嵌入的3球将4球分割成与4球微分同构的2个4流形分量。证明的论据还表明，稳定4球的任意两个同伦微分同态是光滑同位素，如果其中一个微分同态允许局部微分同态变化，则它们是光滑协调的和分段线性同位素。

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Smooth Homotopy 4-Sphere

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.

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来源期刊

WSEAS Transactions on Mathematics Mathematics-Discrete Mathematics and Combinatorics

CiteScore

1.30

自引率

0.00%

发文量

期刊介绍： WSEAS Transactions on Mathematics publishes original research papers relating to applied and theoretical mathematics. We aim to bring important work to a wide international audience and therefore only publish papers of exceptional scientific value that advance our understanding of these particular areas. The research presented must transcend the limits of case studies, while both experimental and theoretical studies are accepted. It is a multi-disciplinary journal and therefore its content mirrors the diverse interests and approaches of scholars involved with linear algebra, numerical analysis, differential equations, statistics and related areas. We also welcome scholarly contributions from officials with government agencies, international agencies, and non-governmental organizations.