Sparse handlebody decompositions and non-finiteness of $g_3=0$
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2020
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| _version_ | 1866910608289431552 |
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| author | Adiprasito, Karim Benedetti, Bruno |
| author_facet | Adiprasito, Karim Benedetti, Bruno |
| contents | 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 $g_3 =0$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2011_08312 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Sparse handlebody decompositions and non-finiteness of $g_3=0$ Adiprasito, Karim Benedetti, Bruno Geometric Topology Combinatorics 57Q15, 57R05, 52B05, 20F05, 57R65 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 $g_3 =0$. |
| title | Sparse handlebody decompositions and non-finiteness of $g_3=0$ |
| topic | Geometric Topology Combinatorics 57Q15, 57R05, 52B05, 20F05, 57R65 |
| url | https://arxiv.org/abs/2011.08312 |