Homology, Homotopy and Applications
Volume 11 (2009)
On structure sets of manifold pairs
Pages: 195 – 222
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.
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