On the space of Fredholm operators

TL;DR

This paper explores the topological structure of unbounded Fredholm operators and their significance in K-theory, also establishing a general continuity result for families of elliptic boundary value problems.

Contribution

It introduces two topologies on the space of unbounded Fredholm operators and demonstrates their relevance in K-theory, along with a general continuity theorem for elliptic boundary problems.

Findings

Defined two topologies on unbounded Fredholm operators

Established K-theoretic relevance of these topologies

Proved a general continuity result for elliptic boundary value families

Abstract

We describe two topologies on the space of unbounded Fredholm operators and we explain their K-theoretic relevance. In the process we also prove a very general result concerning the continuity of families of first order, elliptic boundary value problems.