The K-theory of twisted multipullback quantum odd spheres and complex projective spaces

TL;DR

This paper explores the K-theory of multipullback quantum odd spheres and complex projective spaces, revealing their stable non-isomorphism, classical K-group equivalence, and robustness under twisting.

Contribution

It introduces multipullback quantum spheres and projective spaces with natural actions, analyzing their K-theory and stability under twisting, extending classical results to noncommutative geometry.

Findings

K-groups of quantum spaces match classical counterparts

Quantum line bundles are pairwise stably non-isomorphic

K-groups remain invariant under twisting

Abstract

We find multipullback quantum odd-dimensional spheres equipped with natural $U(1)$-actions that yield the multipullback quantum complex projective spaces constructed from Toeplitz cubes as noncommutative quotients. We prove that the noncommutative line bundles associated to multipullback quantum odd spheres are pairwise stably non-isomorphic, and that the $K$-groups of multipullback quantum complex projective spaces and odd spheres coincide with their classical counterparts. We show that these $K$-groups remain the same for more general twisted versions of our quantum odd spheres and complex projective spaces.