numbers manifest the same properties as the charges carried by elementary particles: a *composition law*, the *alternative of Bose and Fermi statistics* and the *charge conjugation symmetry*. The first example of sectors manifesting these properties has been provided in [@DHR1; @DHR2], known as DHR-analysis, where the authors investigated sharply localized sectors. Namely, a representation $\pi$ of $\mathscr{R}_{\mathcal{K}}$ is a sector of DHR-type whenever its restriction to the spacelike complement ${\mathcal{O}}^\perp$ of any element ${\mathcal{O}}$ of ${\mathcal{K}}$ is unitary equivalent to the vacuum representation $\pi_o$ of the net, in symbols $$\label{Int:1}
\pi|_{\mathcal{R}({\mathcal{O}}^\perp)} \cong \pi_o|_{\mathcal{R}({\mathcal{O}}^\perp)}, 
\qquad {\mathcal{O}}\in{\mathcal{K}}.$$ Although no known charge present in nature is sharply localized, the importance of the DHR-analysis resides in the following reasons. First, it suggests the idea that physically charged sectors might be localized in a more generalized sense with respect to (\[Int:1\]). Secondly, the introduction of powerful techniques based only on the causal structure of the Minkowski space that can be used to investigate other types of localized sectors. A relevant example are the BF-sectors [@BF] which describe charges in purely massive theories. BF-sectors are localized in spacelike cones, which are a family of noncompact regions of ${\mathbb{M}^4}$. In curved spacetimes the nontrivial topology can induce 