# Topological crystalline materials: General formulation, module structure, and wallpaper groups

@inproceedings{Shiozaki2017TopologicalCM, title={Topological crystalline materials: General formulation, module structure, and wallpaper groups}, author={Ken Shiozaki and Masatoshi Sato and Kiyonori Gomi}, year={2017} }

We formulate topological crystalline materials on the basis of the twisted equivariant $K$-theory. Basic ideas of the twisted equivariant $K$-theory is explained with application to topological phases protected by crystalline symmetries in mind, and systematic methods of topological classification for crystalline materials are presented. Our formulation is applicable to bulk gapful topological crystalline insulators/superconductors and their gapless boundary and defect states, as well as bulk… CONTINUE READING

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#### References

##### Publications referenced by this paper.

SHOWING 1-4 OF 4 REFERENCES

## Crossed products by finite groups acting on low dimensional complexes and applications

VIEW 1 EXCERPT

HIGHLY INFLUENTIAL