The infinitesimal multiplicities and orientations of the blow-up set of the Seiberg-Witten equation with multiple spinors

Andriy Haydys

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arXiv · 1607.01763

The infinitesimal multiplicities and orientations of the blow-up set of the Seiberg-Witten equation with multiple spinors

Andriy Haydys

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Abstract

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 Poincar\'{e} dual of the first Chern class of the determinant line bundle. I also obtain a lower bound for the 1-dimensional Hausdorff measure of $Z$.

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BibTeX RIS

Andriy Haydys. 2016-07-06. The infinitesimal multiplicities and orientations of the blow-up set of the Seiberg-Witten equation with multiple spinors. https://arxiv.org/abs/1607.01763

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