Relating VFCs on thin compactifications
Relating VFCs on thin compactifications
复制标题
将 VFC 与薄压实相关
DOI：
10.1007/s00208-019-01861-0
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发表时间：
2018
影响因子：
1.4
通讯作者：
Thomas H. Parker
中科院分区：
文献类型：
--
作者：
Eleny;Thomas H. Parker
在几何分析中出现的许多模空间承认“fredholm分层薄紧化”，因此承认一个相对基本类（RFC），正如作者先前定义的那样。我们扩展了这些结果，强调了RFC的自然性，消除了分层的需要，并证明了三个兼容性结果：RFC定义的不变量与伪循环定义的不变量一致，RFC与切下模空间兼容，并且RFC在定义两者的所有情况下都与Pardon通过隐式地图集构造的虚拟基本类（VFC）一致。
Many moduli spaces that occur in geometric analysis admit “Fredholm-stratified thin compactifications”, and hence admit a relative fundamental class (RFC), as defined previously by the authors. We extend these results, emphasizing the naturality of the RFC, eliminating the need for a stratification, and proving three compatibility results: the invariants defined by the RFC agree with those defined by pseudo-cycles, the RFC is compatible with cutdown moduli spaces, and the RFC agrees with the virtual fundamental class (VFC) constructed by Pardon via implicit atlases in all cases where both are defined.