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arXiv · 2110.14359

Spaces of unbounded Fredholm operators: I. Homotopy equivalences

Marina Prokhorova
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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 self-adjoint operators. Our main results are the following: (1) Natural maps between these four spaces and classical spaces of bounded operators representing K-theory 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 K-theory. (3) The subspace of invertible operators in each of these spaces of unbounded operators is contractible.

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Marina Prokhorova. 2025-03-07. Spaces of unbounded Fredholm operators: I. Homotopy equivalences. https://doi.org/10.1142/s1793525325500116

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