We review the basic concepts and properties of decorated obstruction groups of types LS and LP. Then we establish new relations among these groups and describe the properties of natural maps between different decorated groups. We construct several spectral sequences which contain these decorated groups, and study their connections with the spectral sequences in K-theory for certain quadratic extensions of antistructures. Finally, we introduce the concept of geometric diagram of groups and calculate explicitly the obstruction groups for a diagram formed by finite 2-groups.
Algebraic properties of decorated splitting obstruction groups / Cavicchioli, Alberto; Muranov, Yv; Repovs, D.. - In: BOLLETTINO DELL'UNIONE MATEMATICA ITALIANA. A. - ISSN 0392-4033. - STAMPA. - 4-B (8):(2001), pp. 647-675.
Algebraic properties of decorated splitting obstruction groups
CAVICCHIOLI, Alberto;
2001
Abstract
We review the basic concepts and properties of decorated obstruction groups of types LS and LP. Then we establish new relations among these groups and describe the properties of natural maps between different decorated groups. We construct several spectral sequences which contain these decorated groups, and study their connections with the spectral sequences in K-theory for certain quadratic extensions of antistructures. Finally, we introduce the concept of geometric diagram of groups and calculate explicitly the obstruction groups for a diagram formed by finite 2-groups.
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