\(\Omega\)-Spectrum in topological phases

Abstract

Symmetry-protected topological phases are an active field of research in condensed matter physics. The classification of symmetry-protected topological phases is an important problem in mathematics and theoretical physics. In this paper, a direct approach based on the use of methods of homotopy theory and the theory of infinite loop spaces is proposed to describe the \(\Omega\)-spectra and the generalized cohomology theories arising in the classification of topological phases.