Canonical holomorphic sections of determinant line bundles
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Canonical holomorphic sections of determinant line bundles. / Kaad, Jens; Nest, Ryszard.
I: Journal fur die Reine und Angewandte Mathematik, Bind 746, 2019, s. 67-116.Publikation: Bidrag til tidsskrift › Tidsskriftartikel › fagfællebedømt
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TY - JOUR
T1 - Canonical holomorphic sections of determinant line bundles
AU - Kaad, Jens
AU - Nest, Ryszard
PY - 2019
Y1 - 2019
N2 - 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.
AB - 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.
U2 - 10.1515/crelle-2015-0114
DO - 10.1515/crelle-2015-0114
M3 - Journal article
VL - 746
SP - 67
EP - 116
JO - Journal fuer die Reine und Angewandte Mathematik
JF - Journal fuer die Reine und Angewandte Mathematik
SN - 0075-4102
ER -
ID: 212506589