Compatible Relative Lefschetz Fibrations On Admissible Relative Stein Pairs
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| Format: | Preprint |
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2023
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| author | Yildirim, Yasemin Arikan, M. Firat |
| author_facet | Yildirim, Yasemin Arikan, M. Firat |
| contents | For more than two decades it has been known that any compact Stein surface (of real dimension four) admits a compatible Lefschetz fibration over a two-disk. More recently, Giroux and Pardon have generalized this result by giving a complex geometric proof for the existence of compatible Lefschetz fibrations on Stein domains of any even dimension. As a preparatory step in proving the former, Akbulut and Ozbagci have shown that there exist infinitely many pairwise non-equivalent Lefschetz fibrations on the four-ball by using a result of Lyon constructing fibrations on the complements of (p,q)-torus links in the three-sphere. In this paper, we first extend this result to obtain compatible Lefschetz fibrations on the six-ball whose pages are (p, q, 2)-Brieskorn varieties, and then construct a compatible 'relative' Lefschetz fibrations on any Stein domain (of dimension six) which admit a certain ('admissible') 'relative Stein pair' structure. In particular, we provide a purely topological proof for the existence of Lefschetz fibrations on specific 6-dimensional Stein domains. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2310_15700 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Compatible Relative Lefschetz Fibrations On Admissible Relative Stein Pairs Yildirim, Yasemin Arikan, M. Firat Geometric Topology Symplectic Geometry 57R17, 57R65, 58A05 For more than two decades it has been known that any compact Stein surface (of real dimension four) admits a compatible Lefschetz fibration over a two-disk. More recently, Giroux and Pardon have generalized this result by giving a complex geometric proof for the existence of compatible Lefschetz fibrations on Stein domains of any even dimension. As a preparatory step in proving the former, Akbulut and Ozbagci have shown that there exist infinitely many pairwise non-equivalent Lefschetz fibrations on the four-ball by using a result of Lyon constructing fibrations on the complements of (p,q)-torus links in the three-sphere. In this paper, we first extend this result to obtain compatible Lefschetz fibrations on the six-ball whose pages are (p, q, 2)-Brieskorn varieties, and then construct a compatible 'relative' Lefschetz fibrations on any Stein domain (of dimension six) which admit a certain ('admissible') 'relative Stein pair' structure. In particular, we provide a purely topological proof for the existence of Lefschetz fibrations on specific 6-dimensional Stein domains. |
| title | Compatible Relative Lefschetz Fibrations On Admissible Relative Stein Pairs |
| topic | Geometric Topology Symplectic Geometry 57R17, 57R65, 58A05 |
| url | https://arxiv.org/abs/2310.15700 |