渐近单极模空间的同调稳定性

IF 2.9 3区综合性期刊 Q1 MULTIDISCIPLINARY SCIENCES

Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences Pub Date : 2023-10-01 DOI:10.1098/rspa.2023.0300

Martin Palmer, Ulrike Tillmann

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引用次数: 0

摘要

证明了两种不同类型的渐近单极子模空间的同调稳定性，即框架狄拉克单极子的模空间和理想单极子的模空间。前者是构型空间上的Gibbons-Manton环面束，而后者是通过Borel构造将光纤的每个圆因子替换为单极模空间而得到的。它们在经典单极模空间的部分紧化中形成边界超曲面。我们的结果来自于具有非局部数据的构形空间的一般同调稳定性结果。

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Homology stability for asymptotic monopole moduli spaces

We prove homological stability for two different flavours of asymptotic monopole moduli spaces, namely moduli spaces of framed Dirac monopoles and moduli spaces of ideal monopoles . The former are Gibbons–Manton torus bundles over configuration spaces whereas the latter are obtained from them by replacing each circle factor of the fibre with a monopole moduli space by the Borel construction. They form boundary hypersurfaces in a partial compactification of the classical monopole moduli spaces. Our results follow from a general homological stability result for configuration spaces equipped with non-local data.

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来源期刊

Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 综合性期刊-综合性期刊

CiteScore

6.40

自引率

5.70%

发文量

227

审稿时长

3.0 months

期刊介绍： Proceedings A has an illustrious history of publishing pioneering and influential research articles across the entire range of the physical and mathematical sciences. These have included Maxwell"s electromagnetic theory, the Braggs" first account of X-ray crystallography, Dirac"s relativistic theory of the electron, and Watson and Crick"s detailed description of the structure of DNA.