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arxiv: 1901.06419 · v1 · pith:MFLS4PQInew · submitted 2019-01-16 · 🧮 math-ph · cond-mat.str-el· hep-th· math.AT· math.MP

Invertible phases of matter with spatial symmetry

classification 🧮 math-ph cond-mat.str-elhep-thmath.ATmath.MP
keywords phasesgroupformulainvertiblematterspacesymmetrytopological
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We propose a general formula for the group of invertible topological phases on a space $Y$, possibly equipped with the action of a group $G$. Our formula applies to arbitrary symmetry types. When $Y$ is Euclidean space and $G$ a crystallographic group, the term `topological crystalline phases' is sometimes used for these phases of matter.

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