Open Access
April 2005 Relative groups in surgery theory
Alberto Cavicchioli, Yuri V. Muranov, Fulvia Spaggiari
Bull. Belg. Math. Soc. Simon Stevin 12(1): 109-135 (April 2005). DOI: 10.36045/bbms/1113318134


In this paper we consider various types of relative groups which naturally arise in surgery theory, and describe algebraic properties of them. Then we apply the obtained results to investigate the splitting obstruction groups $LS_*$ and the surgery obstruction groups $LP_*$ for a manifold pair. Finally, we introduce the lower $LS_*$- and $LP_*$-groups, and describe connections between them and the corresponding lower $L_*$-groups and surgery exact sequence.


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Alberto Cavicchioli. Yuri V. Muranov. Fulvia Spaggiari. "Relative groups in surgery theory." Bull. Belg. Math. Soc. Simon Stevin 12 (1) 109 - 135, April 2005.


Published: April 2005
First available in Project Euclid: 12 April 2005

zbMATH: 1072.57025
MathSciNet: MR2134861
Digital Object Identifier: 10.36045/bbms/1113318134

Primary: 19G24 , 19J25 , 57Q10 , 57R67
Secondary: 18F25 , 55U35 , 57R10

Keywords: lower $L$-groups , splitting along a submanifold , splitting obstruction groups , surgery exact sequence , surgery obstruction groups

Rights: Copyright © 2005 The Belgian Mathematical Society

Vol.12 • No. 1 • April 2005
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