基群为二面体的4流形的同伦分类

IF 0.6 3区数学 Q3 MATHEMATICS Algebraic and Geometric Topology Pub Date : 2020-11-06 DOI:10.2140/agt.2022.22.2915

Daniel Kasprowski, John Nicholson, Benjamin Matthias Ruppik

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引用次数: 1

摘要

我们证明了有向庞加莱4-复形的同伦型是由它的二次2型决定的，只要它的基群是有限的并且有一个二面体的Sylow 2-子群。这适用于基本群是SO(3)的有限子群的光滑定向4流形，其例子是具有有限基本群的椭圆曲面。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Homotopy classification of 4–manifolds whose fundamental group is dihedral

We show that the homotopy type of an oriented Poincare 4-complex is determined by its quadratic 2-type provided its fundamental group is finite and has a dihedral Sylow 2-subgroup. This applies in the case of smooth oriented 4-manifolds whose fundamental group is a finite subgroup of SO(3), examples of which are elliptic surfaces with finite fundamental group.

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