Muranov, Yu. V.; Hambleton, I. Projective splitting obstruction groups for one-sided submanifolds. (English. Russian original) Zbl 0953.57017 Sb. Math. 190, No. 10, 1465-1485 (1999); translation from Mat. Sb. 190, No. 10, 65-86 (1999). The authors introduce the concept of a geometric diagram of groups as a natural generalization of the square arising in the splitting problem for a one-sided manifold. A geometric square of groups consists of a commutative square of groups equipped with geometric antistructures in which the horizontal maps are epimorphisms and the vertical maps are inclusions of index \(2\). The authors define the \(LS\)-groups and \(LP\)-groups of a geometric square and study their properties. Fairly complete results are obtained in the case of finite \(2\)-groups. Reviewer: M.Kolster (Hamilton/Ontario) Cited in 2 Documents MSC: 57R67 Surgery obstructions, Wall groups 57Q10 Simple homotopy type, Whitehead torsion, Reidemeister-Franz torsion, etc. 19J25 Surgery obstructions (\(K\)-theoretic aspects) 19G24 \(L\)-theory of group rings 18F25 Algebraic \(K\)-theory and \(L\)-theory (category-theoretic aspects) Keywords:geometric diagrams; surgery obstruction groups; splitting problem PDFBibTeX XMLCite \textit{Yu. V. Muranov} and \textit{I. Hambleton}, Sb. Math. 190, No. 10, 1465--1485 (1999; Zbl 0953.57017); translation from Mat. Sb. 190, No. 10, 65--86 (1999) Full Text: DOI