Smooth Kuranishi atlases with isotropy
Smooth Kuranishi atlases with isotropy
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DOI：
10.2140/gt.2017.21.2725
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发表时间：
2015-08
期刊：
影响因子：
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通讯作者：
D. Mcduff;K. Wehrheim
中科院分区：
文献类型：
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作者：
D. Mcduff;K. Wehrheim
Kuranishi结构在20世纪90年代由福谷和Ono引入，目的是将虚圈分配给不能用几何方法正则化的伪全纯曲线的模空间。他们的核心思想是通过修补局部有限维约简来构建这样一个循环，由有限各向同性群下等变的光滑部分给出。我们的拓扑Kuranishi地图集和微扰建设的情况下，平凡的各向同性的概念的基础上，我们开发了一个理论的Kuranishi地图集和cobordisms，透明地解决了非平凡的各向同性所带来的挑战。我们分配到一个cobordism类的弱Kuranishi图集的虚模循环（VMC -cobordism类的加权分支流形）和虚拟的基本类（VFC -切赫同源类）。
Kuranishi structures were introduced in the 1990s by Fukaya and Ono for the purpose of assigning a virtual cycle to moduli spaces of pseudoholomorphic curves that cannot be regularized by geometric methods. Their core idea was to build such a cycle by patching local finite dimensional reductions, given by smooth sections that are equivariant under a finite isotropy group. Building on our notions of topological Kuranishi atlases and perturbation constructions in the case of trivial isotropy, we develop a theory of Kuranishi atlases and cobordisms that transparently resolves the challenges posed by nontrivial isotropy. We assign to a cobordism class of weak Kuranishi atlases both a virtual moduli cycle (VMC - a cobordism class of weighted branched manifolds) and a virtual fundamental class (VFC - a Cech homology class).