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ISSN (electronic): 1472-2739
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Some results on vector bundle monomorphisms

Daciberg L Gonçalves, Alice K M Libardi and Oziride Manzoli Neto

Algebraic & Geometric Topology 7 (2007) 829–843

arXiv: math.AW/0611679

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)].

Keywords
bordism, normal bordism, stable and nonstable monomorphisms
Mathematical Subject Classification 2000
Primary: 57R90
Secondary: 57R25
References
Publication
Received: 13 November 2006
Revised: 23 March 2007
Accepted: 28 March 2007
Published: 20 June 2007
Authors
Daciberg L Gonçalves
Departamento de Matemática
IME – Universidade de São Paulo
Caixa Postal 66281–Agê ncia Cidade de São Paulo
05311–970
São Paulo–SP
Brazil
Alice K M Libardi
Departamento de Matemática
IGCE – Universidade Estadual Paulista Júlio de Mesquita Filho
Av. 24A, 1515
13506–700
Rio Claro – SP
Brazil
Oziride Manzoli Neto
Departamento de Matemática
ICMC – Universidade de São Paulo
Av. Trabalhador Sãocarlense, 400 – Caixa Postal 668
13560–970
São Carlos – SP
Brazil