论文标题
在合理同拷贝类型的交叉点类型上
On the rational homotopy type of intersection spaces
论文作者
论文摘要
Banagl的交叉路口方法允许在单数集合附近修改某些类型的分层假雌枪，以使理性的Betti数量变化的空间数量与Goresky-Macpherson的交叉点同源物相比，使普遍的Poincaré二元性满足了广义的Poincaré二元性。在一个孤立的奇点的情况下，我们表明偶性同构来自非排定相交的配对，这取决于常规层基本类别的链条代表的选择。在技术方面，由于沙利文（Sullivan），我们使用分段线性多项式差异形式来定义与交叉空间的合适的交换割线代数模型。我们的建筑与Banagl的平滑差分形式的交换界代数建模相交空间的共同体，我们表明这两个代数都是弱等效的。
Banagl's method of intersection spaces allows to modify certain types of stratified pseudomanifolds near the singular set in such a way that the rational Betti numbers of the modified spaces satisfy generalized Poincaré duality in analogy with Goresky-MacPherson's intersection homology. In the case of one isolated singularity, we show that the duality isomorphism comes from a nondegenerate intersection pairing which depends on the choice of a chain representative of the fundamental class of the regular stratum. On the technical side, we use piecewise linear polynomial differential forms due to Sullivan to define a suitable commutative cochain algebra model for intersection spaces. Our construction parallels Banagl's commutative cochain algebra of smooth differential forms modeling intersection space cohomology, and we show that both algebras are weakly equivalent.
