On a construction of some homology $d$-manifolds
Fuente:
arXiv
Salvato in:
| Autori principali: | , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2022
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866912653037797376 |
|---|---|
| author | Basak, Biplab Sarkar, Sourav |
| author_facet | Basak, Biplab Sarkar, Sourav |
| contents | The $g$-vector of a simplicial complex contains a lot of information about the combinatorial and topological structure of that complex. Several classification results regarding the structure of normal pseudomanifolds and homology manifolds have been established concerning the value of $g_2$. It is known that when $g_2=0$, all normal pseudomanifolds of dimensions at least three are stacked spheres. In the cases of $g_2=1$ and $2$, all homology manifolds are polytopal spheres and can be obtained through retriangulation or join operations from the previous ones. In this article, we provide a combinatorial characterization of the homology $d$-manifolds, where $d\geq 3$ and $g_2=3$. These are spheres and can be obtained through operations such as joins, some retriangulations, and connected sums from spheres with $g_2\leq 2$. Furthermore, we have presented a structural result on prime normal $d$-pseudomanifolds with $g_2=3$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2206_01117 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | On a construction of some homology $d$-manifolds Basak, Biplab Sarkar, Sourav Combinatorics Geometric Topology Primary 05E45, Secondary 55U10, 57Q05, 57Q15, 57Q25 The $g$-vector of a simplicial complex contains a lot of information about the combinatorial and topological structure of that complex. Several classification results regarding the structure of normal pseudomanifolds and homology manifolds have been established concerning the value of $g_2$. It is known that when $g_2=0$, all normal pseudomanifolds of dimensions at least three are stacked spheres. In the cases of $g_2=1$ and $2$, all homology manifolds are polytopal spheres and can be obtained through retriangulation or join operations from the previous ones. In this article, we provide a combinatorial characterization of the homology $d$-manifolds, where $d\geq 3$ and $g_2=3$. These are spheres and can be obtained through operations such as joins, some retriangulations, and connected sums from spheres with $g_2\leq 2$. Furthermore, we have presented a structural result on prime normal $d$-pseudomanifolds with $g_2=3$. |
| title | On a construction of some homology $d$-manifolds |
| topic | Combinatorics Geometric Topology Primary 05E45, Secondary 55U10, 57Q05, 57Q15, 57Q25 |
| url | https://arxiv.org/abs/2206.01117 |