On structure sets of manifold pairs

TL;DR

This paper explores the relationships between structure sets of manifold pairs, using an analogy between manifolds with boundary and closed manifold pairs to construct and analyze obstruction groups.

Contribution

It introduces a systematic framework for understanding structure sets of manifold pairs and develops methods to construct and study their associated obstruction groups.

Findings

Established relations between structure sets of manifold pairs.

Constructed obstruction groups for natural maps of structure sets.

Analyzed properties of these obstruction groups.

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.