Topological defects of nematic liquid crystals confined in porous networks

We study the formation of topological defects in nematic liquid crystals confined in open bicontinuous networks produced in glass by femtosecond laser micromachining. We obtain a careful classification of the number and localisation of the defects as a function of the topological properties of the network. Our findings lead to a general formula that predicts the total topological charge in open complex networks, thus complementing the classic Stein-Gauss theorem. Our result provides a justification for the observed multistability of nematics confined in porous networks.