@article{CarlosBiasi2008,
abstract = {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.},
author = {Carlos Biasi, Alice K. M. Libardi, Pedro L. Q. Pergher, Stanisław Spież},
journal = {Bulletin of the Polish Academy of Sciences. Mathematics},
keywords = {ambiental bordism; oriented cobordism group; Euler class; Alexander duality isomorphism; Lefschetz duality isomorphism; Thom class; Thom transversality theorem},
language = {eng},
number = {2},
pages = {177-182},
title = {On the Extension of Certain Maps with Values in Spheres},
url = {http://eudml.org/doc/286489},
volume = {56},
year = {2008},
}
TY - JOUR
AU - Carlos Biasi
AU - Alice K. M. Libardi
AU - Pedro L. Q. Pergher
AU - Stanisław Spież
TI - On the Extension of Certain Maps with Values in Spheres
JO - Bulletin of the Polish Academy of Sciences. Mathematics
PY - 2008
VL - 56
IS - 2
SP - 177
EP - 182
AB - 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.
LA - eng
KW - ambiental bordism; oriented cobordism group; Euler class; Alexander duality isomorphism; Lefschetz duality isomorphism; Thom class; Thom transversality theorem
UR - http://eudml.org/doc/286489
ER -
