论文标题
简单平衡的三个manifolds，Heegaard Floer同源性和Andrews-Curtis猜想
Simple balanced three-manifolds, Heegaard Floer homology and the Andrews-Curtis conjecture
论文作者
论文摘要
第一作者在较早的论文中提出了一个与边界的$ 3 $ manifolds家族的等价概念，称为（简单）平衡的$ 3 $ manifolds，并讨论了Andrews-Curtis等效性的小组演示与上述等价概念之间的类比。在安德鲁斯·库尔蒂（Andrews-Curtis）的猜想中，我们使用Heegaard浮子理论的工具来证明，简单平衡的$ 3 $ - manifolds不在微不足道的等价类中（即$ s^2 \ times的等价类别[-1,1] $）。
The first author introduced a notion of equivalence on a family of $3$-manifolds with boundary, called (simple) balanced $3$-manifolds in an earlier paper and discussed the analogy between the Andrews-Curtis equivalence for group presentations and the aforementioned notion of equivalence. Motivated by the Andrews-Curtis conjecture, we use tools from Heegaard Floer theory to prove that there are simple balanced $3$-manifolds which are not in the trivial equivalence class (i.e. the equivalence class of $S^2\times [-1,1]$).
