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Splitting along a submanifold pair

Published online by Cambridge University Press:  04 March 2008

Rolando Jimenez,
Yu. V. Muranov and
Dušan Repovš
Rolando Jimenez
Affiliation:
rolando@aluxe.matcuer.unam.mxInstituto de Matematicas, UNAM, Avenida Universidad S/N, Col. Lomas de Chamilpa, 62210 Cuernavaca, Morelos, Mexico
Yu. V. Muranov
Affiliation:
ymuranov@mixteco.utm.mxUniversidad Tecnologica de la Mixteca, k.m. 2.5 Carretera Huajuapan-Acatlima, 69000 Huajuapan de Leon, Oaxaca, Mexico
Dušan Repovš
Affiliation:
dusan.repovs@guest.arnes.siInstitute for Mathematics, Physics and Mechanics, University of Ljubljana, Jadranska 19, Ljubljana, Slovenia
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Abstract

The 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.

Keywords

Splitting along submanifoldsurgery of manifoldssurgery and splitting obstruction groupssurgery exact sequenceBrowder-Livesay invariantstructure sets

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