Advances in Theoretical and Mathematical Physics

Volume 24 (2020)

Number 7

The first of two special issues in honor of Cumrun Vafa’s 60th birthday

Invertible phases of matter with spatial symmetry

Pages: 1773 – 1788

DOI: https://dx.doi.org/10.4310/ATMP.2020.v24.n7.a3

Authors

Daniel S. Freed (Department of Mathematics, University of Texas, Austin, Tx., U.S.A.)

Michael J. Hopkins (Department of Mathematics, Harvard University, Cambridge, Massachusetts, U.S.A.)

Abstract

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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This material is based upon work supported by the National Science Foundation under Grant Numbers DMS-1158983, DMS-1160461, DMS-1510417, and DMS-1611957.

Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation.

Published 8 September 2021