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Gapped phases of noninteracting fermions, with and without charge conservation and time-reversal symmetry, are classified using Bott periodicity.
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C. Kane, and E. Mele, “ ℤ 2 \mathbb{Z}_{2} Topological Order and the Quantum Spin Hall Effect,” , Phys. Rev. Lett. 95
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R. Roy, “Topological superfluids with time reversal symmetry,” (2008), arXiv:0803.2868
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L. Fidkowski, and A. Kitaev (2009), in preparation
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