论文标题
无限矢量束的Chern字符
Chern character for infinity vector bundles
论文作者
论文摘要
一般复杂歧管上的相干滑轮不一定通过有限的矢量束复合物具有决议。但是D. Toledo和Y.L.L. TONG表明，可以通过类似于Holomorthic Vector Bundles的链复合物的物体来解决一致的滑轮，其共同关系由相干的无限同型系统控制。在现代语言中，这种物体是通过对全体形态矢量束的链络合物的简单性预言而获得的。我们将Chern字符定义为简单的预发图的地图，通过该图，其造成的连接组成部分恢复了托莱多和Tong的Chern特征。结果，我们的构造将托莱多·汤（Toledo Tong）和奥布莱恩·托莱多（O'Brian Toledo Tong）的定义扩展到了堆栈的设置，尤其是均等环境。即使在复杂的歧管的经典环境中，较高同型组上的诱导地图也提供了新的Chern-Simons和更高的Chern-Simons，可用于相干滑轮的不变性。
Coherent sheaves on general complex manifolds do not necessarily have resolutions by finite complexes of vector bundles. However D. Toledo and Y.L.L. Tong showed that one can resolve coherent sheaves by objects analogous to chain complexes of holomorphic vector bundles, whose cocycle relations are governed by a coherent infinite system of homotopies. In the modern language such objects are obtained by the infinity-sheafification of the simplicial presheaf of chain complexes of holomorphic vector bundles. We define a Chern character as a map of simplicial presheaves, whereby the connected components of its sheafification recovers the Chern character of Toledo and Tong. As a consequence our construction extends Toledo Tong and O'Brian Toledo Tong's definition of the Chern character to the settings of stacks and in particular the equivariant setting. Even in the classical setting of complex manifolds, the induced maps on higher homotopy groups provide new Chern-Simons, and higher Chern-Simons, invariants for coherent sheaves.
