A natural generalization is given of the LS groups of obstructions to splitting in the case, of one-sided manifolds. These LS groups depend functorially on four anti-structures and maps between them, generating a: square of a special; form. The connection between the LS groups and the Wall groups of anti-atnictureS: involved in the diagram is studied. 'Intermediate' LS groups (LS with decorations) are also defined, by analogy with the corresponding Wall groups, and the connection between LS groups with different decorations is studied.
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