Symmetry protected topological phases and generalized cohomology

  • Davide GaiottoEmail author
  • Theo Johnson-Freyd
Open Access
Regular Article - Theoretical Physics


We discuss the classification of SPT phases in condensed matter systems. We review Kitaev’s argument that SPT phases are classified by a generalized cohomology theory, valued in the spectrum of gapped physical systems [20, 23]. We propose a concrete description of that spectrum and of the corresponding cohomology theory. We compare our proposal to pre-existing constructions in the literature.


Effective Field Theories Global Symmetries Topological Field Theories Topological States of Matter 


Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.


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Copyright information

© The Author(s) 2019

Authors and Affiliations

  1. 1.Perimeter Institute for Theoretical PhysicsWaterlooCanada

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