球面余切丛上的Lefschetz纤维化和奇异辛结构
Lefschetz fibrations and exotic symplectic structures on cotangent bundles of spheres; includes Corrigendum
摘要：
我们构造开辛流形，它们在无穷远处是凸的（“刘维流形”），并且对于任意n+1个\geq 3，它们与余切丛T^*S^{n+1}是同构的，但不是辛同构的。这些流形被构造为莱夫谢茨纤维化的全空间，其中纤维和除一个之外的所有消失环都是固定的。我们证明，几乎任何最后一个消失圈的选择都会导致非标准辛结构（产生标准T^*S^{n+1}的选择可以精确确定）。勘误改变了原论文中引理1.1的陈述和证明，纠正了我们原来对流形的同构型的描述。我们还填补了引理1.2的原始证明中的一个空白。
英文摘要：
We construct open symplectic manifolds which are convex at infinity ("Liouville manifolds") and which are diffeomorphic, but not symplectically isomorphic, to cotangent bundles T^*S^{n+1}, for any n+1 \geq 3. These manifolds are constructed as total spaces of Lefschetz fibrations, where the fibre and all but one of the vanishing cycles are fixed. We show that almost any choice of the last vanishing cycle leads to a nonstandard symplectic structure (those choices which yield standard T^*S^{n+1} can be exactly determined). The Corrigendum changes the statement and proof of Lemma 1.1 in the original paper, which corrects our original description of the diffeomorphism type of the manifolds. We also fill a gap in the original proof of Lemma 1.2.
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