Nonexistence of Stein structures on 4-manifolds and maximal Thurston-Bennequin numbers

Autor:	Yasui, Kouichi
Rok vydání:	2015
Předmět:	Mathematics - Geometric Topology Mathematics - Symplectic Geometry 57R55 57R65 57R17 57M25
Druh dokumentu:	Working Paper
Popis:	For a 4-manifold represented by a framed knot in $S^3$, it has been well known that the 4-manifold admits a Stein structure if the framing is less than the maximal Thurston-Bennequin number of the knot. In this paper, we prove either the converse of this fact is false or there exists a compact contractible oriented smooth 4-manifold (with Stein fillable boundary) admitting no Stein structure. Note that an exotic smooth structure on $S^4$ exists if and only if there exists a compact contractible oriented smooth 4-manifold with $S^3$ boundary admitting no Stein structure. Comment: 12 pages, 11 figures, minor corrections, to appear in Journal of Symplectic Geometry
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1508.01491 Zobrazit plný text záznamu View this record from Arxiv