论文标题
霍奇分解和繁殖二元模型
Hodge decompositions and Poincare duality models
论文作者
论文摘要
我们将共同体的完美配对$ n $配对的CDGA $ \ hat V $与CDGA $ v $一起扩展到链级上的$ n $配对，以使$ \ hat v $允许hodge分解，并缩回$ v $ v $ v $ v $保留了同学配对；在这里，我们假设$ v $要么是1连接的，要么是有限类型连接的$ v $，而$ n $是奇怪的。我们表明，$ \ hat v $的杂物分解以自然方式诱导$ v $的差异庞加莱偶性模型。假设$ h（v）$是1连接的，我们将扩展名应用于$ v $的沙利文模型，以证明存在于Lambrechts＆Stanley的$ v $的1个连接的$ V $的1个连接的Poincaré二元模型的“唯一性”；我们在唯一声明中消除了他们的额外假设，包括$ h^2（v）= 0 $如果$ n $奇怪。
We extend a CDGA $V$ with a perfect pairing of degree $n$ on cohomology to a CDGA $\hat V$ with a pairing of degree $n$ on chain level such that $\hat V$ admits a Hodge decomposition and retracts onto $V$ preserving the pairing on cohomology; here we suppose that $V$ is either 1-connected, or that $V$ is connected, of finite type, and $n$ is odd. We show that a Hodge decomposition of $\hat V$ induces a differential Poincaré duality model of $V$ in a natural way. Assuming that $H(V)$ is 1-connected, we apply our extension to a Sullivan model of $V$ in the proof of the existence and "uniqueness" of a 1-connected differential Poincaré duality model of $V$ by Lambrechts & Stanley; we eliminate their extra assumptions in the uniqueness statement, including $H^2(V)=0$ if $n$ is odd.
