The infinitesimal multiplicities and orientations of the blow-up set of the Seiberg-Witten equation with multiple spinors
I construct multiplicies and orientations of tangent cones to any blow-up set $Z$ for the Seiberg-Witten equation with multiple spinors. This is used to prove that $Z$ determines a homology class, which is shown to be equal to the Poincaré dual of the first Chern class of the determinant line bundle. I also obtain a lower bound for the 1-dimensional Hausdorff measure of $Z$.
- Pub Date:
- July 2016
- Mathematics - Geometric Topology;
- Mathematical Physics;
- Mathematics - Differential Geometry
- v5: cosmetic changes mainly v4: extended version, main results clarified, new results added