Homological Lie brackets on moduli spaces and pushforward operations in twisted K-theory

IF 0.8 2区数学 Q2 MATHEMATICS

Journal of Topology Pub Date : 2025-05-29 DOI:10.1112/topo.70025

Markus Upmeier

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引用次数: 0

Abstract

We develop a general theory of pushforward operations for principal $G$ -bundles equipped with a certain type of orientation. In the case $G = B U (1)$ and orientations in twisted K-theory, we construct two pushforward operations, the projective Euler operation, whose existence was conjectured by Joyce, and the projective rank operation. We classify all stable pushforward operations in this context and show that they are all generated by the projective Euler and rank operation. As an application, we construct a graded Lie algebra structure on the homology of a commutative H-space with a compatible $B U (1)$ -action and orientation. These play an important role in the context of wall-crossing formulas in enumerative geometry.

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模空间上的同调李括号与扭曲k理论中的推进运算

我们发展了具有一定定向类型的主G$ G$ -束的推进运算的一般理论。在扭曲k理论中的G= B U (1) $G={B\ maththrm {U}(1)}$和方向的情况下，我们构造了两个推进运算，即投影欧拉运算，其存在性由Joyce猜想；投影秩运算。我们对这种情况下所有稳定的前推运算进行了分类，并证明它们都是由投影欧拉和秩运算生成的。作为一个应用，我们在具有相容B U (1) ${B\mathrm{U}(1)}$ -作用和方向的可交换h空间的同调上构造了一个梯度李代数结构。这些在列举几何中的过墙公式中起着重要的作用。

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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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.