Geodesic
An $H^{3}(G,{\mathbb T})$-valued index of symmetry-protected topological phases with on-site finite group symmetry for two-dimensional quantum spin systems
Forum of Mathematics, Pi, Tome 9 (2021)

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We consider symmetry-protected topological phases with on-site finite group G symmetry $\beta $ for two-dimensional quantum spin systems. We show that they have $H^{3}(G,{\mathbb T})$-valued invariant. 
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     title = {An $H^{3}(G,{\mathbb T})$-valued index of symmetry-protected topological phases with on-site finite group symmetry for two-dimensional quantum spin systems},
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Yoshiko Ogata. An $H^{3}(G,{\mathbb T})$-valued index of symmetry-protected topological phases with on-site finite group symmetry for two-dimensional quantum spin systems. Forum of Mathematics, Pi, Tome 9 (2021). doi: 10.1017/fmp.2021.17

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