论文标题
在具有孤立固定点和分类的定向歧管上的圆环动作图6
Graphs for torus actions on oriented manifolds with isolated fixed points and classification in dimension 6
论文作者
论文摘要
让圆环在带有孤立固定点的紧凑型歧管$ m $上作用，并有一个额外的温和假设，即其各向异性亚策略是可以定向的。我们将歧管的固定点数据（在固定点和各向同性submanifolds上的固定点数据（权重和符号）编码的签名标记的多机关联。我们研究了$ m $及其多编码的操作，（自我）连接的总和和爆炸等。当圆圈组以6维$ m $的形式作用时，我们通过证明我们可以通过连续应用两种操作来将其转换为空图来对其进行分类。特别是，这将分类任何此类歧管的固定点数据。我们通过证明，对于任何这样的流形，我们都可以随身携带固定点上的均值连接总和，$ \ m m i \ m artbb {cp}^3 $以及6维模拟$ z_1 $和$ z_2 $ hirzebruch表面的$ z_1 $和$ z_2 $（以及相反的方向），以在固定点上免费的动作，以在6-- 6-上进行固定点上的固定点。我们还为4维$ M $ $ $ $ $ $ $ M $进行了多个曲线措施分类。
Let a torus act on a compact oriented manifold $M$ with isolated fixed points, with an additional mild assumption that its isotropy submanifolds are orientable. We associate a signed labeled multigraph encoding the fixed point data (weights and signs at fixed points and isotropy submanifolds) of the manifold. We study operations on $M$ and its multigraph, (self) connected sum and blow up, etc. When the circle group acts on a 6-dimensional $M$, we classify such a multigraph by proving that we can convert it into the empty graph by successively applying two types of operations. In particular, this classifies the fixed point data of any such manifold. We prove this by showing that for any such manifold, we can successively take equivariant connected sums at fixed points with itself, $\mathbb{CP}^3$, and 6-dimensional analogue $Z_1$ and $Z_2$ of the Hirzebruch surfaces (and these with opposite orientations) to a fixed point free action on a compact oriented 6-manifold. We also classify a multigraph for a torus action on a 4-dimensional $M$.
