Spaces of unbounded Fredholm operators. I. Homotopy equivalences
Abstract
This paper is devoted to the space of unbounded Fredholm operators equipped with the graph topology, the subspace of operators with compact resolvent, and their subspaces consisting of selfadjoint operators. Our main results are the following: (1) Natural maps between these four spaces and classical spaces of bounded operators representing Ktheory are homotopy equivalences. This provides an alternative proof of a particular case of results of Joachim. (2) The subspace of unbounded essentially positive Fredholm operators represents odd Ktheory. (3) The subspace of invertible operators in each of these spaces of unbounded operators is contractible.
 Publication:

arXiv eprints
 Pub Date:
 October 2021
 arXiv:
 arXiv:2110.14359
 Bibcode:
 2021arXiv211014359P
 Keywords:

 Mathematics  KTheory and Homology;
 Mathematics  Algebraic Topology;
 Mathematics  Differential Geometry
 EPrint:
 v2: 24 pages