Iterated Browder-Livesay invariants and the oozing problem
type: Item
instance of: scholarly article
title: Iterated Browder-Livesay invariants and the oozing problem
zbMATH Open document ID: 0673.57026
DOI: 10.1007/BF01137681
author: A. F. Kharshiladze
published in: Mathematical Notes
publication date: 1987-01-01T00:00:00Z
review text: The Browder-Livesay-Wall surgery theory for codimension 1 submanifolds with nontrivial normal bundle has obstruction groups \(LN_*\). In the case when the fundamental group of the manifold and the submanifold are the same, the fundamental group of the complement is an index 2 subgroup, and the LN-groups are the algebraic l-groups of the corresponding ring with antistructure. This theory can be applied to the detection of the elements in the ordinary surgery obstruction group \(L_*(G)\), which are the closed manifold surgery obstructions. This note investigates the iteration of this procedure for a sequence of such codimension 1 submanifolds, corresponding to a sequence of index 2 subgroups. Theorem 1 states that an element with nontrivial image in one of the relevant LN groups cannot be a closed manifold surgery obstruction. Theorem 2 states that a homotopy equivalence with nontrivial image in one of the relevant LN groups cannot be split along that submanifold.
Mathematics Subject Classification ID: 57R67
Mathematics Subject Classification ID: 18F25
zbMATH DE Number: 4102098
zbMATH Keywords: Browder-Livesay-Wall surgery theory
zbMATH Keywords: codimension 1 submanifolds with nontrivial normal bundle
zbMATH Keywords: surgery obstruction group
zbMATH Keywords: index 2 subgroups
zbMATH Keywords: homotopy equivalence
MaRDI profile type: Publication
cites work: The L-Theory of Twisted Quadratic Extensions
cites work: Q5624419
cites work: Q3969588
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description: scientific article; zbMATH DE number 4102098