发表机构
Adelaide University（阿德莱德大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文用等变Seiberg–Witten理论重新证明了正定4-流形上有限循环群作用的不动点集和切向表示与线性作用的等变连通和一致，并确定了所有等变线丛的权重。
AI 中文摘要
设$X$为一个闭、光滑、可定向、正定的$4$-流形，且$H_1(X; \mathbb{Z}) = 0$。设$p$为一个素数，并假设$G = \mathbb{Z}_p$光滑地作用在$X$上（若$p=2$，我们还要求$G$在$H^2(X; \mathbb{Z})$上的作用满足一个假设）。利用等变Yang–Mills理论，Hambleton–Lee和Hambleton–Tanase证明了（在单连通情形下）不动点集和切向迷向表示与$G$线性作用在$\mathbb{CP}^2$的若干拷贝的等变连通和上的相应对象一致。我们利用等变Seiberg–Witten理论给出了这一结果的新证明。此外，我们还确定了$X$上所有等变线丛的权重，表明这些权重同样与$\mathbb{CP}^2$上线性作用的等变连通和的权重一致。
英文摘要
Let $X$ be a closed, smooth, orientable, positive definite $4$-manifold with $H_1(X ; \mathbb{Z}) = 0$. Let $p$ be a prime and suppose that $G = \mathbb{Z}_p$ acts smoothly on $X$ (if $p=2$ we also require an assumption on how $G$ acts on $H^2(X ; \mathbb{Z})$). Using equivariant Yang--Mills theory, Hambleton--Lee and Hambleton--Tanase proved (in the simply-connected case) that the fixed point set and tangential isotropy representations coincide with that of an equivariant connected sum of copies of $\mathbb{CP}^2$ on which $G$ acts linearly. We give a new proof of this result using equivariant Seiberg--Witten theory. Furthermore we also determine the weights of all equivariant line bundles on $X$, showing that these likewise coincide with that of an equivariant connected sum of linear actions on $\mathbb{CP}^2$.
Comments44 pages
