%0 Journal Article %T The adjunction problem over torsion-free groups %A Max Forester %A Colin Rourke %J Mathematics %D 2004 %I arXiv %R 10.1073/pnas.0502940102 %X In this note we prove injectivity and relative asphericity for "layered" systems of equations over torsion-free groups, when the exponent matrix is invertible over Z. We also give elementary geometric proofs of results due to Bogley-Pride and Serre that are used in the proof of the main theorem. %U http://arxiv.org/abs/math/0412274v2