$K_0$ groups of Connes' $\Theta$-deformed $m$-planes

TL;DR

This paper computes the K_0 groups of Connes' Theta-deformed m-planes and their smooth variants, establishing that they are all isomorphic to the integers, thus providing insight into their algebraic topology.

Contribution

It demonstrates that the K_0 groups of Connes' Theta-deformed m-planes and their smooth versions are all isomorphic to Z, revealing their algebraic structure.

Findings

K_0 groups are isomorphic to Z

Results apply to both deformed and smooth m-planes

Provides algebraic classification of these noncommutative spaces

Abstract

We show that the $K_0$ groups of Connes' $\Theta$-deformed $m$-planes and their smooth versions are all $\mathbb{Z}$.