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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.

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)
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