论文标题
关于脊柱开放式书籍分解的符号填充ii：全体形态曲线和分类
On symplectic fillings of spinal open book decompositions II: Holomorphic curves and classification
论文作者
论文摘要
在两部分系列的第二篇论文中，我们证明，每当接触3键符合平面页面上的脊柱开放式书籍分解时，它（弱，弱，强和/或精确）的符号和斯坦因填充物就可以将其分类至变形等效，以leffschetz纤维的差异性类别的类别。这将第三作者的先前结果扩展到了更广泛的触点歧管，我们在此处通过将所有定向的圆圈捆绑包的强和强大填充物与非区域$ s^1 $ -INVARIANT接触结构进行分类。进一步的结果包括SFT中ECH接触不变性和代数扭转的新的消失标准，某些不可取向圆圈的填充物的分类以及对实际维度四个维度方面的Stein结构的变形类别的一般“象征性的准屈服”结果。
In this second paper of a two-part series, we prove that whenever a contact 3-manifold admits a uniform spinal open book decomposition with planar pages, its (weak, strong and/or exact) symplectic and Stein fillings can be classified up to deformation equivalence in terms of diffeomorphism classes of Lefschetz fibrations. This extends previous results of the third author to a much wider class of contact manifolds, which we illustrate here by classifying the strong and Stein fillings of all oriented circle bundles with non-tangential $S^1$-invariant contact structures. Further results include new vanishing criteria for the ECH contact invariant and algebraic torsion in SFT, classification of fillings for certain non-orientable circle bundles, and a general "symplectic quasiflexibility" result about deformation classes of Stein structures in real dimension four.
