射影空间稳定流形的同构性

IF 0.8 2区数学 Q2 MATHEMATICS

Journal of Topology Pub Date : 2023-09-06 DOI:10.1112/topo.12313

Ruizhi Huang, Stephen Theriault

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引用次数: 5

摘要

我们研究了具有投影空间的流形的连通和的同伦性，认为这是稳定流形的一种典型方法。特别地，我们给出了一个流形在被投影空间稳定后的循环仿射分解，并给出了具体的例子。为了做到这一点，我们通过在远离经典J$J$-同态的图像顺序的定位后显示循环仿射分解，来追踪在某些乘积流形上的运算的同伦论中的影响。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

Homotopy of manifolds stabilized by projective spaces

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Homotopy of manifolds stabilized by projective spaces

We study the homotopy of the connected sum of a manifold with a projective space, viewed as a typical way to stabilize manifolds. In particular, we show a loop homotopy decomposition of a manifold after stabilization by a projective space, and provide concrete examples. To do this, we trace the effect in homotopy theory of surgery on certain product manifolds by showing a loop homotopy decomposition after localization away from the order of the image of the classical $J$ -homomorphism.

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来源期刊

Journal of Topology 数学-数学

CiteScore

2.00

自引率

9.10%

发文量

审稿时长

>12 weeks

期刊介绍： The Journal of Topology publishes papers of high quality and significance in topology, geometry and adjacent areas of mathematics. Interesting, important and often unexpected links connect topology and geometry with many other parts of mathematics, and the editors welcome submissions on exciting new advances concerning such links, as well as those in the core subject areas of the journal. The Journal of Topology was founded in 2008. It is published quarterly with articles published individually online prior to appearing in a printed issue.