$L^p$-上同调、热半群与分层空间
$L^p$-cohomology, heat semigroup and stratified spaces
AI总结：
本文研究有限体积不完备黎曼流形上$L^p$与$L^2$上同调群之间的映射关系，并将其应用于分层伪流形和孤立奇点复射影簇的曲率与交点上同调。
摘要：
设$(M,g)$是一个有限体积的不完备黎曼流形，且$2\leq p<\infty$。在本文的第一部分，我们证明在某些假设下，$L^p$-微分形式空间到$L^2$-微分形式空间的包含映射在相应的$L^p$与$L^2$上同调群之间诱导出单射/满射映射。然后在第二部分，我们将这些结果应用于紧致Thom-Mather分层伪流形以及仅具有孤立奇点的复射影簇的曲率和交点上同调，给出多种应用。
英文摘要：
Let $(M,g)$ be an incomplete Riemannian manifold of finite volume and let $2\leq p<\infty$. In the first part of this paper we prove that under certain assumptions the inclusion of the space of $L^p$-differential forms into that of $L^2$-differential forms gives rise to an injective/surjective map between the corresponding $L^p$ and $L^2$ cohomology groups. Then in the second part we provide various applications of these results to the curvature and the intersection cohomology of compact Thom-Mather stratified pseudomanifolds and complex projective varieties with only isolated singularities.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
