具有边界的4-流形的非光滑同胚

IF 1.5 1区数学 Q1 MATHEMATICS

Advances in Mathematics Pub Date : 2025-03-06 DOI:10.1016/j.aim.2025.110191

Daniel Galvin , Roberto Ladu

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引用次数: 0

摘要

构造了具有边界的光滑4流形的非光滑自同胚的第一个例子，这些流形的边界固定且对同调起着平凡的作用。作为推论，我们构造了具有边界的4流形的自微分同构，该边界固定边界并对同构起平凡的作用，但不能同位素于边界的一个环中支持的任何自微分同构，特别是不能同位素于任何广义Dehn扭转。

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Non-smoothable homeomorphisms of 4-manifolds with boundary

We construct the first examples of non-smoothable self-homeomorphisms of smooth 4-manifolds with boundary that fix the boundary and act trivially on homology. As a corollary, we construct self-diffeomorphisms of 4-manifolds with boundary that fix the boundary and act trivially on homology but cannot be isotoped to any self-diffeomorphism supported in a collar of the boundary and, in particular, are not isotopic to any generalised Dehn twist.

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来源期刊

Advances in Mathematics 数学-数学

CiteScore

2.80

自引率

5.90%

发文量

497

审稿时长

7.5 months

期刊介绍： Emphasizing contributions that represent significant advances in all areas of pure mathematics, Advances in Mathematics provides research mathematicians with an effective medium for communicating important recent developments in their areas of specialization to colleagues and to scientists in related disciplines.