论文标题
可还原的3个manifolds
Equivariant Heegaard genus of reducible 3-manifolds
论文作者
论文摘要
具有有限的组$ g $ diffemorphisms的作用的3个manifold $ m $的高度heegaard属是以$ m $ $ $ $ $ $ $ $ $的差异为差异的最小属。尽管可简化的歧管的heegaard分裂是可降低的，尽管$ m $可还原，但有一个均等的必需球体，但我们表明，在等效的连接总和下，近似雄性的heegaard属可能是超级加性，加性或亚addive的。使用薄的位置理论，用于三维轨道，我们在可还原流形的近似远处属上建立了尖锐的界限，类似于隧道数量所知。
The equivariant Heegaard genus of a 3-manifold $M$ with the action of a finite group $G$ of diffeomorphisms is the smallest genus of an equivariant Heegaard splitting for $M$. Although a Heegaard splitting of a reducible manifold is reducible and although if $M$ is reducible, there is an equivariant essential sphere, we show that equivariant Heegaard genus may be super-additive, additive, or sub-additive under equivariant connected sum. Using a thin position theory for 3-dimensional orbifolds, we establish sharp bounds on the equivariant Heegaard genus of reducible manifolds, similar to those known for tunnel number.
