On the Extension of Certain Maps with Values in Spheres

• Autorzy: Carlos Biasi , Alice K. M. Libardi , Pedro L. Q. Pergher , Stanisław Spież
• Języki publikacji: EN

Abstrakty

EN

Let E be an oriented, smooth and closed m-dimensional manifold with m ≥ 2 and V ⊂ E an oriented, connected, smooth and closed (m-2)-dimensional submanifold which is homologous to zero in E. Let $S^{n-2} ⊂ Sⁿ$ be the standard inclusion, where Sⁿ is the n-sphere and n ≥ 3. We prove the following extension result: if $h: V → S^{n-2}$ is a smooth map, then h extends to a smooth map g: E → Sⁿ transverse to $S^{n-2}$ and with $g^{-1}(S^{n-2}) = V$. Using this result, we give a new and simpler proof of a theorem of Carlos Biasi related to the ambiental bordism question, which asks whether, given a smooth closed n-dimensional manifold E and a smooth closed m-dimensional submanifold V ⊂ E, one can find a compact smooth (m+1)-dimensional submanifold W ⊂ E such that the boundary of W is V.

Kategorie tematyczne

• 55S36: Extension and compression of mappings
• 55S35: Obstruction theory

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2008
• Tom: 56
• Numer: 2
• Strony: 177-182

Daty

wydano

2008

Twórcy

autor

Carlos Biasi

• Departamento de Matemática, ICMC-USP - Campus de São Carlos, Caixa Postal 668, São Carlos, SP 13560-970, Brazil

autor

Alice K. M. Libardi

• Departamento de Matemática, IGCE-UNESP - Campus de Rio Claro, Rio Claro, SP 13506-700, Brazil

autor

Pedro L. Q. Pergher

• Departamento de Matemática, Universidade Federal de São Carlos, Caixa Postal 676, São Carlos, SP 13565-905, Brazil

autor

Stanisław Spież

• Institute of Mathematics, Polish Academy of Sciences, Śniadeckich 8, P.O. Box 21, 00-956 Warszawa, Poland

Identyfikatory

DOI

10.4064/ba56-2-8