In this talk I will review the common appearance of torsion in solids as well as some new developments. Torsion typically appears in condensed matter physics associated to topological defects known as dislocations. Now we are beginning to uncover new aspects of the coupling of torsion to materials. Recently, a dissipationless viscosity has been studied in the quantum Hall effect. I will connect this viscosity to a 2+1-d torsion Chern-Simons term and discuss possible thought experiments in which this could be measured. If time permits, I will briefly discuss a new topological defect in 3+1-d, a torsional skyrmion, which does not require a lattice deformation to exist in solids. If present, torsional skyrmions are likely to impact the propagation of electrons in materials with strong spin-orbit coupling such as topological insulators and spin-orbit coupled semiconductors.
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