Homology, Homotopy and Applications

Volume 11 (2009)

Number 2

On structure sets of manifold pairs

Pages: 195 – 222

DOI: http://dx.doi.org/10.4310/HHA.2009.v11.n2.a10

Authors

Matija Cencelj (Institute of Mathematics, Physics and Mechanics, University of Ljubljana, Slovenia)

Yuri V. Muranov (Physical Department, Vitebsk State University, Vitebsk, Belarus)

Dušan Repovš (Institute of Mathematics, Physics and Mechanics, University of Ljubljana, Slovenia)

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.

Keywords

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

2010 Mathematics Subject Classification

18F25, 19J25, 55T99, 57R67, 58A35

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