@article {Fiorenza2016,
	title = {Z2 Invariants of Topological Insulators as Geometric Obstructions},
	journal = {Communications in Mathematical Physics},
	volume = {343},
	number = {3},
	year = {2016},
	month = {May},
	pages = {1115{\textendash}1157},
	abstract = {<p>We consider a gapped periodic quantum system with time-reversal symmetry of fermionic (or odd) type, i.e. the time-reversal operator squares to $-\mathbb{1}$. We investigate the existence of periodic and time-reversal invariant Bloch frames in dimensions 2 and 3. In 2d, the obstruction to the existence of such a frame is shown to be encoded in a $\mathbb{Z}_2$-valued topological invariant, which can be computed by a simple algorithm. We prove that the latter agrees with the Fu-Kane index. In 3d, instead, four $\mathbb{Z}_2$ invariants emerge from the construction, again related to the Fu-Kane-Mele indices. When no topological obstruction is present, we provide a constructive algorithm yielding explicitly a periodic and time-reversal invariant Bloch frame. The result is formulated in an abstract setting, so that it applies both to discrete models and to continuous ones.</p>},
	issn = {1432-0916},
	doi = {10.1007/s00220-015-2552-0},
	url = {https://doi.org/10.1007/s00220-015-2552-0},
	author = {Domenico Fiorenza and Domenico Monaco and Gianluca Panati}
}
