论文标题
稀疏的句柄分解和$ g_3 = 0 $的非精力
Sparse handlebody decompositions and non-finiteness of $g_3=0$
论文作者
论文摘要
我们证明，PL歧管在索引$ \ le K $的手柄上承认，并且仅当$ m $是$ k $ stacked时，即它承认所有$（d-k-1）$ - faces均在$ \ partial m $上。 我们用它来解决Kalai在2008年提出的问题：在任何高于四个的维度上，都有无限的许多同源性，其中$ G_3 = 0 $。
We prove that a PL manifold admits a handle decomposition into handles of index $\le k$ if and only if $M$ is $k$-stacked, i.e., it admits a PL triangulation in which all $(d-k-1)$-faces are on $\partial M$. We use this to solve a problem posed in 2008 by Kalai: In any dimension higher than four, there are infinitely many homology-spheres with $g_3 =0$.
