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Some results on extension of maps and applications

Part of: Homotopy groups Differential topology Homotopy theory

Published online by Cambridge University Press:  16 January 2019

Carlos Biasi ,
Alice K. M. Libardi ,
Thiago de Melo  and
Edivaldo L. dos Santos
Carlos Biasi
Affiliation:
Departamento de Matemática, Instituto de Ciências Matemáticas e de Computação, São Paulo University - Campus de São Carlos, 13560-970, São Carlos, SP, Brazil (biasi@icmc.usp.br)
Alice K. M. Libardi
Affiliation:
Departamento de Matemática, São Paulo State University (Unesp), Institute of Geosciences and Exact Sciences, Rio Claro, Bela Vista, 13506-700, Rio Claro, SP, Brazil (alice.libardi@unesp.br; thiago.melo@unesp.br)
Thiago de Melo
Affiliation:
Departamento de Matemática, São Paulo State University (Unesp), Institute of Geosciences and Exact Sciences, Rio Claro, Bela Vista, 13506-700, Rio Claro, SP, Brazil (alice.libardi@unesp.br; thiago.melo@unesp.br)
Edivaldo L. dos Santos
Affiliation:
Departamento de Matematica, Federal University of São Carlos, Rodovia Washington Luiz. km 235 São Carlos, SP, Brazil (edivaldo@dm.ufscar.br)
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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 SO-equivalent.

Keywords

extension of mapsobstructionhomotopyvector bundle

MSC classification

Primary: 57R42: Immersions
Secondary: 55Q10: Stable homotopy groups 55P60: Localization and completion
Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 149 , Issue 6 , December 2019 , pp. 1465 - 1472
Copyright
Copyright © Royal Society of Edinburgh 2019 

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Footnotes

Dedicated to Professor Gilberto Loibel, in memorian.

References

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