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arXiv · 1301.5811

The kernel bundle of a holomorphic Fredholm family

Thomas Krainer·Gerardo A. Mendoza
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Abstract

Let $\Y$ be a smooth connected manifold, $\Sigma\subset\C$ an open set and $(\sigma,y)\to\scrP_y(\sigma)$ a family of unbounded Fredholm operators $D\subset H_1\to H_2$ of index 0 depending smoothly on $(y,\sigma)\in \Y\times \Sigma$ and holomorphically on $\sigma$. We show how to associate to $\scrP$, under mild hypotheses, a smooth vector bundle $\kerb\to\Y$ whose fiber over a given $y\in \Y$ consists of classes, modulo holomorphic elements, of meromorphic elements $\phi$ with $\scrP_y\phi$ holomorphic. As applications we give two examples relevant in the general theory of boundary value problems for elliptic wedge operators.

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Thomas Krainer, Gerardo A. Mendoza. 2013-01-24. The kernel bundle of a holomorphic Fredholm family. https://arxiv.org/abs/1301.5811

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