ON INTERSECTION AND TRANSVERSALITY OF MAPS

• Autor(a) principal: Libardi, Alice K. M. [UNESP]
• Data de Publicação: 2023
• Outros Autores: Mattos, Denise de, Santos, Edivaldo L. dos
• Tipo de documento: Artigo
• Idioma: eng
• Título da fonte: Repositório Institucional da UNESP
• Texto Completo: http://dx.doi.org/10.1090/proc/16123; http://hdl.handle.net/11449/245620
• topic: Extension of maps; obstruction; homotopy; transversality

Given a smooth map fV: V-+ K with f*V(nu K) = nu V, a gen-eral question arises: under which conditions there exists a smooth extension f : M-+ N of fV such that f is transverse to K and f-1(K) = V, where M, N are smooth closed manifolds of dimension m and n, V, K are closed submanifolds of M and N, respectively, of same codimension and nu K, nu V are the normal bundles of K in N and V in M, respectively. In this paper, we give conditions to the existence of extensions, by using bordism intersection pro d-uct. Moreover, we present an interesting and non-trivial example illustrating the systematic construction of such extensions, skeletonwise.