Splitting along a submanifold pair

Details Splitting along a submanifold pair Splitting along a submanifold pair

2006-08-29

arxiv.org/abs/math/0608730v1

Journal of K-Theory 2 (2008), 385-404.

Mathematics

Geometric Topology

K-theory, to appear

Scientific paper

10.1017/is008001011jkt031

The paper introduces a group $LSP$ of obstructions for splitting a homotopy equivalence along a pair of submanifolds. We develop exact sequences relating the $LSP$-groups with various surgery obstruction groups for manifold triple and structure sets arising from triples of manifolds. 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.

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