Canonical holomorphic sections of determinant line bundles

Publikation: Bidrag til tidsskriftTidsskriftartikelForskningfagfællebedømt

Jens Kaad, Ryszard Nest

We investigate the analytic properties of torsion isomorphisms (determinants) of mapping cone triangles of Fredholm complexes. Our main tool is a generalization to Fredholm complexes of the perturbation isomorphisms constructed by R. Carey and J. Pincus for Fredholm operators. A perturbation isomorphism is a canonical isomorphism of determinants of homology groups associated to a finite rank perturbation of Fredholm complexes. The perturbation isomorphisms allow us to establish the invariance properties of the torsion isomorphisms under finite rank perturbations. We then show that the perturbation isomorphisms provide a holomorphic structure on the determinant lines over the space of Fredholm complexes. Finally, we establish that the torsion isomorphisms and the perturbation isomorphisms provide holomorphic sections of certain determinant line bundles.
OriginalsprogEngelsk
TidsskriftJournal fur die Reine und Angewandte Mathematik
Vol/bind746
Sider (fra-til)67-116
ISSN0075-4102
DOI
StatusUdgivet - 2019

ID: 212506589