Homology, Homotopy and Applications

On structure sets of manifold pairs

Matija Cencelj, Yuri V. Muranov, and Dušan Repovš

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Abstract

In this paper we systematically describe relations between various structure sets which arise naturally for pairs of compact topological manifolds with boundary. Our consideration is based on a deep analogy between the case of a compact manifold with boundary and the case of a closed manifold pair. This approach also gives a possibility to construct the obstruction groups for natural maps of various structure sets and to investigate their properties.

Article information

Source
Homology Homotopy Appl., Volume 11, Number 2 (2009), 195-222.

Dates
First available in Project Euclid: 27 January 2011

Permanent link to this document
https://projecteuclid.org/euclid.hha/1296138518

Mathematical Reviews number (MathSciNet)
MR2591918

Zentralblatt MATH identifier
1185.57030

Subjects
Primary: 57R67: Surgery obstructions, Wall groups [See also 19J25] 19J25: Surgery obstructions [See also 57R67] 55T99: None of the above, but in this section 58A35: Stratified sets [See also 32S60] 18F25: Algebraic $K$-theory and L-theory [See also 11Exx, 11R70, 11S70, 12- XX, 13D15, 14Cxx, 16E20, 19-XX, 46L80, 57R65, 57R67]

Keywords
Surgery on manifolds surgery on manifold pairs surgery obstruction groups splitting obstruction groups surgery exact sequence structure sets normal invariants

Citation

Cencelj, Matija; Muranov, Yuri V.; Repovš, Dušan. On structure sets of manifold pairs. Homology Homotopy Appl. 11 (2009), no. 2, 195--222. https://projecteuclid.org/euclid.hha/1296138518


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