论文标题
$ l^p $ subyatix单数空间的Poincaré二元性
Poincaré duality for $L^p$ cohomology on subanalytic singular spaces
论文作者
论文摘要
我们研究了$ \ mathbb {r}^n $（不一定是紧凑）的有限的亚分析子手机上的$ l^p $差分表格的庞加莱二重性问题。我们表明，当$ p $足够接近$ 1 $时，那么这种子manifold的$ l^p $共同体对其单一同源性是同构的。在$ p $大的情况下，我们表明$ l^p $共同体对交叉同源性是双重的。结果，我们可以推断出$ l^p $共同体是Poincaré二重为$ l^q $同居的，如果$ p $和$ q $是彼此之间的共轭，而$ p $足够大。
We investigate the problem of Poincaré duality for $L^p$ differential forms on bounded subanalytic submanifolds of $\mathbb{R}^n$ (not necessarily compact). We show that, when $p$ is sufficiently close to $1$ then the $L^p$ cohomology of such a submanifold is isomorphic to its singular homology. In the case where $p$ is large, we show that $L^p$ cohomology is dual to intersection homology. As a consequence, we can deduce that the $L^p$ cohomology is Poincaré dual to $L^q$ cohomology, if $p$ and $q$ are Hölder conjugate to each other and $p$ is sufficiently large.
