the net.'
author:
- |
    Giuseppe Ruzzi\
    \
    \
title: 'Homotopy of posets, net-cohomology and superselection sectors in globally hyperbolic spacetimes'
---

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Introduction {#Int}
============

The present paper is concerned with the study of charged superselection sectors in globally hyperbolic spacetimes in the framework of the algebraic approach to quantum field theory [@Ha; @HK]. The basic object of this approach is the abstract net *of local observables* $\mathscr{R}_{\mathcal{K}}$, namely the correspondence $${\mathcal{K}}\ni{\mathcal{O}}\rightarrow\mathcal{R}({\mathcal{O}}),$$ which associates to any element ${\mathcal{O}}$ of a family ${\mathcal{K}}$ of relatively compact open regions of the spacetime ${\mathcal{M}}$, considered as a fixed background manifold, the $\mathrm{C}^*-$algebra $\mathcal{R}({\mathcal{O}})$ generated by all the observables which are measurable within ${\mathcal{O}}$. Sectors are unitary equivalence classes of irreducible representations of this net, the labels distinguishing different classes are the quantum numbers. The study of physically meaningful sectors of the net of local observables, and how to select them, is the realm of the theory of superselection sectors.\
One of the main results of superselection sectors theory has been the demonstration that in Minkowski space ${\mathbb{M}^4}$, among the representations of the net of local observables it is possible to select a family of sectors whose quantum 