论文标题
使用理性同源圈构建理性同源球
Using rational homology circles to construct rational homology balls
论文作者
论文摘要
由Akbulut-Larson的Brieskorn Spher构造有限的合理同源性4球的构造，我们探索了限制了理性同源性圈子的3个模型，并利用它们来构建无限的理性同源性家庭3 spheres bound bountion bountion tobrational同源性的界限。这些理性同源性中的一些三个角度是整数同源性的新示例3键，它们构成了理性同源性4球，但不绑定整数同源性4球。 In particular, we find infinite families of torus bundles over the circle that bound rational homology circles, provide a simple method for constructing more general plumbed 3-manifolds that bound rational homology circles, and show that, for example, $-1$-surgery along any unknotting number one knot $K$ with a positive crossing that can be switched to unknot $K$ bounds a rational homology 4-ball.
Motivated by Akbulut-Larson's construction of Brieskorn spheres bounding rational homology 4-balls, we explore plumbed 3-manifolds that bound rational homology circles and use them to construct infinite families of rational homology 3-spheres that bound rational homology 4-balls. Some of these rational homology 3-spheres are new examples of integer homology 3-spheres that bound rational homology 4-balls, but do not bound integer homology 4-balls. In particular, we find infinite families of torus bundles over the circle that bound rational homology circles, provide a simple method for constructing more general plumbed 3-manifolds that bound rational homology circles, and show that, for example, $-1$-surgery along any unknotting number one knot $K$ with a positive crossing that can be switched to unknot $K$ bounds a rational homology 4-ball.
