Some results on extension of maps and applications
C. Biasi, A. Libardi, T. Melo, E. dos Santos

TL;DR
This paper explores the extension of maps via obstruction theory, classifies homotopy classes, and applies these results to vector bundle equivalence and homotopy of embeddings up to surgery.
Contribution
It introduces a non classical approach to map extension, provides a new proof of Adachi's theorem, and relates embeddings' homotopy to normal bundle equivalence.
Findings
Classification of homotopy classes of maps.
A simple proof of Adachi's theorem on vector bundles.
Conditions under which embeddings are homotopic up to surgery.
Abstract
This paper concerns extension of maps using obstruction theory under a non classical viewpoint. It is given a classification of homotopy classes of maps and as an application it is presented a simple proof of a theorem by Adachi about equivalence of vector bundles. Also it is proved that, under certain conditions, two embeddings are homotopic up to surgery if and only if the respective normal bundles are -equivalent.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Advanced Topology and Set Theory · Algebraic Geometry and Number Theory
