Brunnian links are determined by their complements

If L_1 and L_2 are two Brunnian links with all pairwise linking numbers 0, then we show that L_1 and L_2 are equivalent if and only if they have homeomorphic complements. In particular, this holds for all Brunnian links with at least three components. If L_1 is a Brunnian link with all pairwise linking numbers 0, and the complement of L_2 is homeomorphic to the complement of L_1, then we show that L_2 may be obtained from L_1 by a sequence of twists around unknotted components. Finally, we show that for any positive integer n, an algorithm for detecting an n-component unlink leads immediately to an algorithm for detecting an unlink of any number of components. This algorithmic generalization is conceptually simple, but probably computationally impractical.Comment: Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol1/agt-1-7.abs.htm

Origin of charge density at LaAlO3-on-SrTiO3 hetero-interfaces; possibility of intrinsic doping

As discovered by Ohtomo et al., a large sheet charge density with high mobility exists at the interface between SrTiO3 and LaAlO3. Based on transport, spectroscopic and oxygen-annealing experiments, we conclude that extrinsic defects in the form of oxygen vacancies introduced by the pulsed laser deposition process used by all researchers to date to make these samples is the source of the large carrier densities. Annealing experiments show a limiting carrier density. We also present a model that explains the high mobility based on carrier redistribution due to an increased dielectric constant.Comment: 14 pages, 3 figures, 1 table; accepted for publication in Phys. Rev. Lett