Manifolds not containing Gompf nuclei
英文摘要：
In this note we show that there are 4-manifolds not containing Gompf nucleus $N_2$; in this way we answer Problem 4.98 of Kirby's problem list in the negative.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
继续探索
相关论文
Nuclei and exotic 4-manifolds
We introduce a new generalization of Gompf nuclei and give applications. We construct infinitely many exotic smooth structures for a large class of compact 4-manifolds with boundary, regarding topological invariants. We prove that a large class of closed 3-manifolds (including disjoint unions of Stein fillable 3-manifolds) bound compact connected oriented 4-manifolds which admit infinitely many smooth structures. To detect smooth structures, we introduce a relative genus function. As a side result, we show that log transform and knot surgery of 4-manifolds do not admit any Stein structure, und…
math.GTmath.SG
Minimality and symplectic sums
Let X_1, X_2 be symplectic 4-manifolds containing symplectic surfaces F_1,F_2 of identical positive genus and opposite squares. Let Z denote the symplectic sum of X_1 and X_2 along the F_k. Using relative Gromov--Witten theory, we determine precisely when the symplectic 4-manifold Z is minimal (i.e., cannot be blown down); in particular, we prove that Z is minimal unless either: one of the X_k contains a (-1)-sphere disjoint from F_k; or one of the X_k admits a ruling with F_k as a section. As special cases, this proves a conjecture of Stipsicz asserting the minimality of fiber sums of Lefsche…
math.GTmath.SG
