The Browder-Livesay invariants provide obstructions to the realization of elements of Wall groups by normal maps of closed manifolds. A generalization of the iterated Browder-Livesay invariants is proposed and properties of the invariants obtained are described. The generalized definition makes it possible to investigate the relationship between a normal map and its restriction to a submanifold and clarifies the relationship between the Browder-Livesay invariants and the Browder-Quinn groups of obstructions to surgery on filtered manifolds. Several theorems describing a relationship between a normal map and its restriction to a submanifold are proved.
On iterated Browder-Livesay invariants / Cavicchioli, Alberto; F., Hegenbarth; Muranov, Y. u. V.; Spaggiari, Fulvia. - In: MATHEMATICAL NOTES. - ISSN 1067-9073. - STAMPA. - 86:(2009), pp. 196-215. [10.1134/S0001434609070232]
On iterated Browder-Livesay invariants
CAVICCHIOLI, Alberto;SPAGGIARI, Fulvia
2009
Abstract
The Browder-Livesay invariants provide obstructions to the realization of elements of Wall groups by normal maps of closed manifolds. A generalization of the iterated Browder-Livesay invariants is proposed and properties of the invariants obtained are described. The generalized definition makes it possible to investigate the relationship between a normal map and its restriction to a submanifold and clarifies the relationship between the Browder-Livesay invariants and the Browder-Quinn groups of obstructions to surgery on filtered manifolds. Several theorems describing a relationship between a normal map and its restriction to a submanifold are proved.
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