A vanishing theorem for Donaldson invariants
A vanishing theorem for Donaldson invariants
复制标题
唐纳森不变量的消失定理
DOI：
10.2307/2160921
复制
发表时间：
1995
期刊：
影响因子：
--
通讯作者：
P. Lisca
中科院分区：
文献类型：
--
作者：
P. Lisca
给出一个光滑单连通4流形M，证明了如果M内有一个光滑嵌入的2环面T，那么M的SU(2)-Donaldson不变量在2-同调类集合上消失，所有同调类都与(T)正交，并且至少有两个是(T)的倍。由此推导出光滑嵌入环面对若干代数曲面的2-同调类的可表示性的阻碍，并计算了若干具有边界的4-流形的自微分同态群。
Given a smooth simply connected 4-manifold M, we prove that if there is a smoothly embedded 2-torus T inside M, then the SU(2)-Donaldson invariants of M vanish on collections of 2-homology classes, all of which are orthogonal to (T) and at least two of which are multiples of (T) . From this we deduce obstructions to the representability of 2-homology classes of some algebraic surfaces by smoothly embedded tori, and we compute the group of self-diffeomorphisms of certain 4-manifolds with boundary.