Splitting along a submanifold pair
Copyright policy )Splitting along a submanifold pair
AbstractThe paper introduces a group LSP of obstructions to splitting a homotopy equivalence along a pair of submanifolds. We develop exact sequences relating the LSP-groups with various surgery obstruction groups for a manifold triple and structure sets arising from a manifold triple. The natural map from the surgery obstruction group of the ambient manifold to the LSP-group provides an invariant when elements of the Wall group are not realized by normal maps of closed manifolds. Some LSP-groups are computed precisely.
- National Autonomous University of Mexico Mexico
- University of Ljubljana Slovenia
- UNIVERZA V LJUBLJANI Slovenia
- Technological University of the Mixteca Mexico
\(L\)-theory of group rings, 18F25, 19G24, surgery and splitting obstruction groups, surgery exact sequence, surgery of manifolds, 19J25, Geometric Topology (math.GT), Triangulating, 57R67; 19J25; 57Q10; 19G24; 18F25, Surgery obstructions, Wall groups, Mathematics - Geometric Topology, 57Q10, FOS: Mathematics, structure sets, Algebraic Topology (math.AT), Algebraic \(K\)-theory and \(L\)-theory (category-theoretic aspects), Browder-Livesay invariant, Mathematics - Algebraic Topology, 57R67, splitting along submanifold, Surgery obstructions (\(K\)-theoretic aspects)
\(L\)-theory of group rings, 18F25, 19G24, surgery and splitting obstruction groups, surgery exact sequence, surgery of manifolds, 19J25, Geometric Topology (math.GT), Triangulating, 57R67; 19J25; 57Q10; 19G24; 18F25, Surgery obstructions, Wall groups, Mathematics - Geometric Topology, 57Q10, FOS: Mathematics, structure sets, Algebraic Topology (math.AT), Algebraic \(K\)-theory and \(L\)-theory (category-theoretic aspects), Browder-Livesay invariant, Mathematics - Algebraic Topology, 57R67, splitting along submanifold, Surgery obstructions (\(K\)-theoretic aspects)
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