Algebraic & Geometric Topology

Some results on vector bundle monomorphisms

Daciberg Lima Gonçalves, Alice Libardi, and Oziride Manzoli

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Abstract

In this paper we use the singularity method of Koschorke [Lecture Notes in Math. 847 (1981)] to study the question of how many different nonstable homotopy classes of monomorphisms of vector bundles lie in a stable class and the percentage of stable monomorphisms which are not homotopic to stabilized nonstable monomorphisms. Particular attention is paid to tangent vector fields. This work complements some results of Koschorke [Lecture Notes in Math. 1350, 1988, Topology Appl. 75 (1997)], Libardi–Rossini [Proc. of the XI Brazil. Top. Meeting 2000] and Libardi–do Nascimento–Rossini [Revesita de Mátematica e Estatística 21 (2003)].

Article information

Source
Algebr. Geom. Topol., Volume 7, Number 2 (2007), 829-843.

Dates
Received: 13 November 2006
Revised: 23 March 2007
Accepted: 28 March 2007
First available in Project Euclid: 20 December 2017

Permanent link to this document
https://projecteuclid.org/euclid.agt/1513796708

Digital Object Identifier
doi:10.2140/agt.2007.7.829

Mathematical Reviews number (MathSciNet)
MR2336243

Zentralblatt MATH identifier
1162.57023

Subjects
Primary: 57R90: Other types of cobordism [See also 55N22]
Secondary: 57R25: Vector fields, frame fields

Keywords
bordism normal bordism stable and nonstable monomorphisms

Citation

Gonçalves, Daciberg Lima; Libardi, Alice; Manzoli, Oziride. Some results on vector bundle monomorphisms. Algebr. Geom. Topol. 7 (2007), no. 2, 829--843. doi:10.2140/agt.2007.7.829. https://projecteuclid.org/euclid.agt/1513796708


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References

  • L D Borsari, D L Gonçalves, The first (co)homology group with local coefficients (2005) preprint
  • U Koschorke, Vector fields and other vector bundle morphisms – a singularity approach, Lecture Notes in Mathematics 847, Springer, Berlin (1981)
  • U Koschorke, The singularity method and immersions of $m$–manifolds into manifolds of dimensions $2m{-}2$, $2m{-}3$ and $2m{-}4$, from: “Differential topology (Siegen, 1987)”, Lecture Notes in Mathematics 1350, Springer, Berlin (1988) 188–212
  • U Koschorke, Nonstable and stable monomorphisms of vector bundles, Topology Appl. 75 (1997) 261–286
  • U Koschorke, Complex and real vector bundle monomorphisms, Topology Appl. 91 (1999) 259–271
  • A K M Libardi, V M do Nascimento, I C Rossini, The cardinality of some normal bordism groups and its applications, Rev. Mat. Estatí st. 21 (2003) 107–114
  • A K M Libardi, I C Rossini, Enumeration of nonstable monomorphisms: the even case, from: “XI Brazilian Topology Meeting (Rio Claro, 1998)”, World Sci. Publ., River Edge, NJ (2000) 80–84
  • D Randall, J Daccach, Cobordismo Normal e Aplicacoes, Notas do Instituto de Ciências Matemáticas de São Carlos, ICMC-USP (1988)