论文标题
关于叶子的手术
Surgery On Foliations
论文作者
论文摘要
在本文中，我们建立了两种手术理论和两种白头扭转，用于叶子。首先，我们构建了一个有界的手术理论和有界的白头扭转，以对应于Connes的叶子代数在操作员代数的K理论中，从某种意义上说，手术理论和索引理论之间存在类比，而Novikov构想手术对叶子进行了类似于Folied Novied novikov novikov inoveration in Novikov tosection和P.Baum的构想构想的构想。该手术理论将叶子拓扑分类。其次，我们为叶子构建了有界的几何手术，这是对手术阻塞的概括和有界的几何形状扭转的概括。该手术理论中的分类包括叶子的里曼尼亚指标的规格，直至准等轴测图。我们陈述了Borel猜想的叶子，该构想解决了S.Weinberger \ cite {Wein}提出的问题，并在某些几何兴趣的情况下对其进行了验证。
In this paper, we set up two surgery theories and two kinds of Whitehead torsion for foliations. First, we construct a bounded surgery theory and bounded Whitehead torsion for foliations, which correspond to the Connes' foliation algebra in the K-theory of operator algebras, in the sense that there is an analogy between surgery theory and index theory, and a Novikov Conjecture for bounded surgery on foliations in analogy with the foliated Novikov conjecture of P.Baum and A.Connes in operator theory. This surgery theory classifies the leaves topologically. Secondly, we construct a bounded geometry surgery for foliations, which is a generalization of blocked surgery, and a bounded geometry Whitehead torsion. The classifications in this surgery theory include the specification of the Riemannian metrics of the leaves up to quasi=isometry. We state Borel conjectures for foliations, which solves a problem posed by S.Weinberger \cite{Wein}, and verify these in some cases of geometrical interest.
