论文标题
旋转伪依仪上的正标曲率：基本组和次要不变性
Positive Scalar Curvature on Spin Pseudomanifolds: the Fundamental Group and Secondary Invariants
论文作者
论文摘要
在本文中，我们继续研究深度标态曲率（PSC）指标在深度-1 thom thom thom thommath的分层空间$m_σ$带有奇异层的$βM$（正编成阳性的封闭形式）和等于$ l $的相关链接，是平滑的紧凑型歧管。我们简短地称其为$ l $ fif的奇异性。在适当的自旋假设下，我们为存在呈正标曲率的楔形指标提供了必要的指数理论条件。除此之外，$ l $是一个正面标量曲率的简单连接的均匀空间，$ l = g/h $，半密切的lie组$ g $ $ g $由ISOMERTIOS在$ L $上进行过渡性，我们在这些必要条件也足够的情况下进行了调查。我们的主要结果是，即使$m_σ$和$βM$不仅连接，我们的条件确实足以满足大量示例。我们还研究了此类PSC指标的空间，并表明它经常分为许多COBORDISM类。
In this paper we continue the study of positive scalar curvature (psc) metrics on a depth-1 Thom-Mather stratified space $M_Σ$ with singular stratum $βM$ (a closed manifold of positive codimension) and associated link equal to $L$, a smooth compact manifold. We briefly call such spaces manifolds with $L$-fibered singularities. Under suitable spin assumptions we give necessary index-theoretic conditions for the existence of wedge metrics of positive scalar curvature. Assuming in addition that $L$ is a simply connected homogeneous space of positive scalar curvature, $L=G/H$, with the semisimple compact Lie group $G$ acting transitively on $L$ by isometries, we investigate when these necessary conditions are also sufficient. Our main result is that our conditions are indeed sufficient for large classes of examples, even when $M_Σ$ and $βM$ are not simply connected. We also investigate the space of such psc metrics and show that it often splits into many cobordism classes.
