2019/10/05 by Taniguchi, Masaki
#FOS: Mathematics #Geometric Topology (math.GT)
paper · doi:10.48550/arxiv.1910.02234
For a given smooth 2-knot in S4, 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 Poincaré homology 3-sphere as a Seifert hypersurface has at least four irreducible SU(2)-representations of its knot group. This result is false in the topological category. The proof uses a quantitative formulation of instanton Floer homology. 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.