Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2023
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2302.02355 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866909290892099584 |
|---|---|
| author | Basak, Biplab Sarkar, Sourav |
| author_facet | Basak, Biplab Sarkar, Sourav |
| contents | Numerous structural findings of homology manifolds have been derived in various ways in relation to $g_2$-values. The homology $4$-manifolds with $g_2\leq 5$ are characterized combinatorially in this article. It is well-known that all homology $4$-manifolds for $g_2\leq 2$ are polytopal spheres. We demonstrate that homology $4$-manifolds with $g_2\leq 5$ are triangulated spheres and are derived from triangulated 4-spheres with $g_2\leq 2$ by a series of connected sum, bistellar 1- and 2-moves, edge contraction, edge expansion, and edge flipping operations. We establish that the above inequality is optimally attainable, i.e., it cannot be extended to $g_2 = 6$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2302_02355 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A structure theorem for homology 4-manifolds with $g_2\leq 5$ Basak, Biplab Sarkar, Sourav Geometric Topology Combinatorics Primary 05E45, Secondary 05C30, 57Q15, 57Q25 Numerous structural findings of homology manifolds have been derived in various ways in relation to $g_2$-values. The homology $4$-manifolds with $g_2\leq 5$ are characterized combinatorially in this article. It is well-known that all homology $4$-manifolds for $g_2\leq 2$ are polytopal spheres. We demonstrate that homology $4$-manifolds with $g_2\leq 5$ are triangulated spheres and are derived from triangulated 4-spheres with $g_2\leq 2$ by a series of connected sum, bistellar 1- and 2-moves, edge contraction, edge expansion, and edge flipping operations. We establish that the above inequality is optimally attainable, i.e., it cannot be extended to $g_2 = 6$. |
| title | A structure theorem for homology 4-manifolds with $g_2\leq 5$ |
| topic | Geometric Topology Combinatorics Primary 05E45, Secondary 05C30, 57Q15, 57Q25 |
| url | https://arxiv.org/abs/2302.02355 |