Simply connectedness of spaces of tight frames

2025/08/04 by Mare, Augustin-Liviu
#14M15 #42C15 #Differential Geometry (math.DG) #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2508.02484

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.

Citations

• Optimization and the Topology of Spaces of Parseval Frames
• Connectivity properties of the Schur-Horn map for real Grassmannians
• Connectivity and Irreducibility of Algebraic Varieties of Finite Unit Norm Tight Frames
• Manifold structure of spaces of spherical tight frames
• Steepest descent on real flag manifolds
• Doubly Stochastic Matrices and the Diagonal of a Rotation Matrix

Related

• Connectivity and Irreducibility of Algebraic Varieties of Finite Unit Norm Tight Frames
• Path-connectedness and topological closure of some sets related to the non-compact Stiefel manifold
• Manifold structure of spaces of spherical tight frames
• Tight frames over the quaternions and equiangular lines
• Constructions of biangular tight frames and their relationships with equiangular tight frames