Sparse handlebody decompositions and non-finiteness of $g_3=0$

Karim Adiprasito; Bruno Benedetti

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arXiv · 2011.08312

Sparse handlebody decompositions and non-finiteness of $g_3=0$

Karim Adiprasito·Bruno Benedetti

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Abstract

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 $g_3 =0$.

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Karim Adiprasito, Bruno Benedetti. 2020-11-16. Sparse handlebody decompositions and non-finiteness of $g_3=0$. https://arxiv.org/abs/2011.08312

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