Seifert hypersurfaces of 2-knots and Chern–Simons functional
Masaki Taniguchi
Institute of Physical and Chemical Research (RIKEN), Wako, Japan
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Abstract
For a given smooth 2-knot in , 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.
Cite this article
Masaki Taniguchi, Seifert hypersurfaces of 2-knots and Chern–Simons functional. Quantum Topol. 13 (2022), no. 2, pp. 335–405
DOI 10.4171/QT/165