Replacing a graph clasper by tree claspers

Clasper 一致性、Whitney 塔与重复 Milnor 不变量

Clasper Concordance, Whitney towers and repeating Milnor invariants

本文证明链环在 4-球中界定度为 k 的 Whitney 塔等价于与平凡链环 $C_k$-一致，并利用重复扭曲 Whitney 塔分类了扭曲自 $C_k$-一致性，基于 Milnor 和 Arf 不变量。

Symplectically replacing plumbings with Euler characteristic 2 4-manifolds

We introduce new symplectic cut-and-paste operations that generalize the rational blowdown. In particular, we will define $k$-replaceable plumbings to be those that, heuristically, can be symplectically replaced by Euler characteristic $k$ 4-manifolds. We will then classify 2-replaceable linear plumbings, construct 2-replaceable plumbing trees, and use one such tree to construct a symplectic exotic $\mathbb{C}P^2\#6\overline{\mathbb{C}P^2}$.