Geodesic
Some results on vector bundle monomorphisms
Gonçalves, Daciberg Lima1 ; Libardi, Alice2 ; Manzoli, Oziride3
1Departamento de Matemática, IME – Universidade de São Paulo, Caixa Postal 66281–Agê ncia Cidade de São Paulo, 05311–970, São Paulo–SP, Brazil
2Departamento de Matemática, IGCE – Universidade Estadual Paulista Júlio de Mesquita Filho, Av. 24A, 1515, 13506–700, Rio Claro – SP, Brazil
3Departamento de Matemática, ICMC – Universidade de São Paulo, Av. Trabalhador Sãocarlense, 400 – Caixa Postal 668, 13560–970, São Carlos – SP, Brazil
Algebraic and Geometric Topology, Tome 7 (2007) no. 2, pp. 829-843
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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)].

DOI : 10.2140/agt.2007.7.829
Keywords: bordism, normal bordism, stable and nonstable monomorphisms

Gonçalves, Daciberg Lima  1   ; Libardi, Alice  2   ; Manzoli, Oziride  3

1 Departamento de Matemática, IME – Universidade de São Paulo, Caixa Postal 66281–Agê ncia Cidade de São Paulo, 05311–970, São Paulo–SP, Brazil
2 Departamento de Matemática, IGCE – Universidade Estadual Paulista Júlio de Mesquita Filho, Av. 24A, 1515, 13506–700, Rio Claro – SP, Brazil
3 Departamento de Matemática, ICMC – Universidade de São Paulo, Av. Trabalhador Sãocarlense, 400 – Caixa Postal 668, 13560–970, São Carlos – SP, Brazil 
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Gonçalves, Daciberg Lima; Libardi, Alice; Manzoli, Oziride. Some results on vector bundle monomorphisms. Algebraic and Geometric Topology, Tome 7 (2007) no. 2, pp. 829-843. doi: 10.2140/agt.2007.7.829

[1] L D Borsari, D L Gonçalves, The first (co)homology group with local coefficients, (2005)

[2] U Koschorke, Vector fields and other vector bundle morphisms – a singularity approach, Lecture Notes in Mathematics 847, Springer (1981)

[3] 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 (1988) 188

[4] U Koschorke, Nonstable and stable monomorphisms of vector bundles, Topology Appl. 75 (1997) 261

[5] U Koschorke, Complex and real vector bundle monomorphisms, Topology Appl. 91 (1999) 259

[6] A K M Libardi, V M Do Nascimento, I C Rossini, The cardinality of some normal bordism groups and its applications, Rev. Mat. Estatíst. 21 (2003) 107

[7] 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

[8] D Randall, J Daccach, Cobordismo Normal e Aplicacoes, Notas do Instituto de Ciências Matemáticas de São Carlos, ICMC-USP (1988)

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