A NOTE ON OPEN 3-MANIFOLDS SUPPORTING FOLIATIONS BY PLANES

Autor(es)

Biasi, Carlos ^[1] ; Maquera, Carlos ^[1]

Afiliação do(s) autor(es)

^[1] Univ Sao Paulo, Inst Ciencia Matemat & Comp, Dept Matemat, BR-13560970 Sao Carlos, SP - Brazil

• Tipo de documento: Artigo Científico
• Fonte: Proceedings of the American Mathematical Society; v. 140, n. 3, p. 961-969, MAR 2012.
• Citações Web of Science: 0

Resumo

We show that if N, an open connected n-manifold with finitely generated fundamental group, is C-2 foliated by closed planes, then pi(1)(N) is a free group. This implies that if pi(1)(N) has an abelian subgroup of rank greater than one, then F has at least a nonclosed leaf. Next, we show that if N is three dimensional with fundamental group abelian of rank greater than one, then N is homeomorphic to T-2 x R. Furthermore, in this case we give a complete description of the foliation. (AU)

• Processo FAPESP: 09/17493-4 - Sistemas dinâmicos definidos por ações de Rk
• Beneficiário: Carlos Alberto Maquera Apaza
• Modalidade de apoio: Auxílio à Pesquisa - Regular
• Processo FAPESP: 08/57607-6 - Topologia algébrica geométrica e diferencial
• Beneficiário: Daciberg Lima Gonçalves
• Modalidade de apoio: Auxílio à Pesquisa - Temático