Simply connectedness of spaces of tight frames

TL;DR

This paper investigates the topological property of simple connectedness in spaces of complex tight frames, including finite unit-norm tight frames, viewed as elements of complex Stiefel manifolds.

Contribution

It identifies a class of spaces of complex tight frames that are simply connected, expanding understanding of their topological structure.

Findings

Spaces of finite unit-norm tight frames are simply connected.

Certain classes of complex tight frames form simply connected spaces.

The work relates tight frames to complex Stiefel manifolds.

Abstract

Complex tight frames can be canonically viewed as elements of a complex Stiefel manifold. We present a class of spaces of such frames which are simply connected relative to the subspace topology. To this class belongs the space of finite unit-norm tight frames.