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We propose that symmetry protected topological (SPT) phases with crystalline symmetry are formulated by equivariant generalized homologies $h^G_n(X)$ over a real space manifold $X$ with $G$ a crystalline symmetry group.
Cohomologie modulo 2 des complexes d’eilenberg-maclane
Jean-Pierre Serre · 1953
Earlier work this paper cites.
Two soluble models of an antiferromagnetic chain
Elliott Lieb, Theodore Schultz, and Daniel Mattis · 1961
Earlier work this paper cites.
Generalized homology theories
George W. Whitehead · 1962
Earlier work this paper cites.
Equivariant cohomology theories
Glen E. Bredon · 1967
Earlier work this paper cites.
The geometry of spherical space form groups
Peter B Gilkey · 1989
Earlier work this paper cites.
Topological gauge theories and group cohomology
Robbert Dijkgraaf and Edward Witten · 1990
Earlier work this paper cites.
Equivariant homotopy and cohomology theory: Dedicated to the memory of Robert J. Piacenza
J Peter May, LG Lewis, Robert John Piacenza, M Cole, G Comezana, S Costenoble, Anthony D Elmendorf, and JPC Greenlees · 1996
Earlier work this paper cites.
Nonstandard symmetry classes in mesoscopic normal-superconducting hybrid structures
Alexander Altland and Martin R. Zirnbauer · 1997
Earlier work this paper cites.
Commensurability, excitation gap, and topology in quantum many-particle systems on a periodic lattice
Masaki Oshikawa · 2000
Earlier work this paper cites.
Theta-terms in nonlinear sigma-models
A.G. Abanov and P.B. Wiegmann · 2000
Earlier work this paper cites.
Unpaired majorana fermions in quantum wires
A Yu Kitaev · 2001
Earlier work this paper cites.
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Allen Hatcher · 2002
Earlier work this paper cites.
Sufficient conditions for topological order in insulators
MB Hastings · 2005
Earlier work this paper cites.
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Akira Kōno and Dai Tamaki · 2006
Earlier work this paper cites.
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Andreas P. Schnyder, Shinsei Ryu, Akira Furusaki, and Andreas W. W. Ludwig · 2008
Earlier work this paper cites.
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Jeffrey C. Y. Teo, Liang Fu, and C. L. Kane · 2008
Earlier work this paper cites.
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Xiao-Liang Qi and Shou-Cheng Zhang · 2008
Earlier work this paper cites.
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Ying Ran, Ashvin Vishwanath, and Dung-Hai Lee · 2008
Earlier work this paper cites.
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Zheng-Cheng Gu and Xiao-Gang Wen · 2009
Earlier work this paper cites.
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Alexei Kitaev · 2009
Earlier work this paper cites.
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Xie Chen, Zheng-Cheng Gu, and Xiao-Gang Wen · 2010
Earlier work this paper cites.
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Earlier work this paper cites.
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Earlier work this paper cites.
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Norbert Schuch, David Pérez-García, and Ignacio Cirac · 2011
Earlier work this paper cites.
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Xie Chen, Zheng-Cheng Gu, and Xiao-Gang Wen · 2011
Earlier work this paper cites.
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Lukasz Fidkowski and Alexei Kitaev · 2011
Earlier work this paper cites.
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Liang Fu · 2011
Earlier work this paper cites.
Complete classification of one-dimensional gapped quantum phases in interacting spin systems
Xie Chen, Zheng-Cheng Gu, and Xiao-Gang Wen · 2011
Earlier work this paper cites.
Braiding statistics approach to symmetry-protected topological phases
Michael Levin and Zheng-Cheng Gu · 2012
Earlier work this paper cites.
Theory and classification of interacting integer topological phases in two dimensions: A chern-simons approach
Yuan-Ming Lu and Ashvin Vishwanath · 2012
Earlier work this paper cites.
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Michael F Atiyah and Friedrich Hirzebruch · 2012
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Xie Chen, Zheng-Cheng Gu, Zheng-Xin Liu, and Xiao-Gang Wen · 2013
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Daniel S. Freed and Gregory W. Moore · 2013
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