Fredholm complexes of Hilbert C*-modules
Operator Algebras
2025-05-13 v1 K-Theory and Homology
Abstract
We investigate complexes of Hilbert C*-modules, which are cochain complexes with (unbounded) regular operators between Hilbert C*-modules as differential maps. In particular, we provide various equivalent characterizations of the Fredholm property for such complexes of Hilbert C*-modules, and we define the Fredholm index taking values in the K-theory group of the C*-algebra. Among other properties of this index, we prove the stability under small or relatively compact perturbations, and we obtain alternative expressions for the index under the existence of a (weak or strong) Hodge decomposition.
Keywords
Cite
@article{arxiv.2505.07568,
title = {Fredholm complexes of Hilbert C*-modules},
author = {Brian Villegas-Villalpando and Koen van den Dungen},
journal= {arXiv preprint arXiv:2505.07568},
year = {2025}
}