In this paper we consider various types of relative groups which naturally arise in surgery theory, and describe algebraic properties of them. Then we apply the obtained results to investigate the splitting obstruction groups LS* and the surgery obstruction groups LP* for a manifold pair. Finally, we introduce the lower LS*- and LP*-groups, and describe connections between them and the corresponding lower L-*-groups and surgery exact sequence.
Relative groups in surgery theory / Cavicchioli, Alberto; Yv, Muranov; Spaggiari, Fulvia. - In: BULLETIN OF THE BELGIAN MATHEMATICAL SOCIETY SIMON STEVIN. - ISSN 1370-1444. - STAMPA. - 12:1(2005), pp. 109-135. [10.36045/bbms/1113318134]
Relative groups in surgery theory
CAVICCHIOLI, Alberto;SPAGGIARI, Fulvia
2005
Abstract
In this paper we consider various types of relative groups which naturally arise in surgery theory, and describe algebraic properties of them. Then we apply the obtained results to investigate the splitting obstruction groups LS* and the surgery obstruction groups LP* for a manifold pair. Finally, we introduce the lower LS*- and LP*-groups, and describe connections between them and the corresponding lower L-*-groups and surgery exact sequence.
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