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

Karim Adiprasito; Bruno Benedetti

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

Geometric Topology 2024-09-19 v3 Combinatorics

Authors: Karim Adiprasito , Bruno Benedetti

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 $g_3 =0$ .

Keywords

pl manifold handle decomposition k-stacked homology sphere g3=0 triangulation

Cite

@article{arxiv.2011.08312,
  title  = {Sparse handlebody decompositions and non-finiteness of $g_3=0$},
  author = {Karim Adiprasito and Bruno Benedetti},
  journal= {arXiv preprint arXiv:2011.08312},
  year   = {2024}
}

Comments

5 pages; revised version; improved exposition; fixed typos. This preprint will be later merged into a survey "Combinatorial Aspects of PL Topology", in preparation

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

Abstract

Keywords

Cite

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