For a given smooth 2-knot in the 4-space, we relate the existence of a smooth Seifert hypersurface of a certain class to the existence of irreducible SU(2)-representations of its knot group. For example, we see that any smooth 2-knot having the Poincar ́e homology 3-sphere as a Seifert hypersurface has at least four irreducible SU(2)-representations of its knot group. This result can not be proved in the topological category. The proof uses a quantitative formulation of instanton Floer homology. Moreover, using similar techniques, we also obtain similar results about codimension-1 embeddings of homology 3-spheres into closed definite 4-manifolds and a fixed point type theorem for instanton Floer homology.

中文翻译：

---

2 结的 Seifert 超曲面和 Chern-Simons 泛函

对于 4 空间中给定的光滑 2 结，我们将某个类的光滑 Seifert 超曲面的存在与其结群的不可约 SU(2) 表示的存在联系起来。例如，我们看到任何具有 Poincar ́e 同调 3 球面作为 Seifert 超曲面的光滑 2 结都具有其结组的至少四个不可约 SU(2) 表示。这个结果不能在拓扑范畴内得到证明。证明使用了瞬时 Floer 同调的定量公式。此外，使用类似的技术，我们还获得了关于将同调 3 球体的 codimension-1 嵌入到封闭的定 4 流形和瞬时 Floer 同调的不动点类型定理的类似结果。