La science et l'hypothèse
《La science et l'hypothèse》 · 第 204–205 页 · Section 6.1，Example 6.1.3（包括 kinky handle、标架与各级 tower 的构造）
The case of 2-handles with self-plumbings, or kinky handles [C], is of independent interest because of its importance in Freedman’s work on topological 4-manifolds [F], [FQ]. The natural convention for framings is that attaching a kinky handle to a 4-manifold \(X\) should look the same as attaching an ordinary handle on the level of intersection forms. That is, we twist the product framing of \(\partial D^2\times0\subset\partial D^2\times D^2\) by twice the signed number of self-plumbings, and match this new framing with the given one on the attaching circle in \(\partial X\). […] Observe that if we attach 2-handles to 0-framed meridians of the dotted circles, we obtain a standard 2-handle attached to the same framed curve \(K\). If we instead attach kinky handles to these 0-framed meridians, we obtain a 2-stage Casson tower \(T_2\) attached to \(K\). Repeating the process with the new kinky handles yields a 3-stage tower \(T_3\), and so on. Taking the infinite union of \(T_2\subset T_3\subset T_4\subset\cdots\), one obtains a Casson handle (after removing all boundary except the attaching region of the original kinky handle \(T_1\)).