TY - JOUR
T1 - Foliated vector fields without periodic orbits
AU - Peralta-Salas, D.
AU - del Pino, Á.
AU - Presas, F.
PY - 2016/7
Y1 - 2016/7
N2 - In this article parametric versions of Wilson’s plug and Kuperberg’s plug are discussed. We show that there is a weak homotopy equivalence induced by the inclusion between the space of non-singular vector fields tangent to a foliation and its subspace comprised of those without closed orbits, as long as the leaves of the foliation have dimension at least 3. We contrast this with the case of foliations by surfaces in 3-manifolds.
AB - In this article parametric versions of Wilson’s plug and Kuperberg’s plug are discussed. We show that there is a weak homotopy equivalence induced by the inclusion between the space of non-singular vector fields tangent to a foliation and its subspace comprised of those without closed orbits, as long as the leaves of the foliation have dimension at least 3. We contrast this with the case of foliations by surfaces in 3-manifolds.
UR - http://www.scopus.com/inward/record.url?eid=2-s2.0-84983616759&partnerID=MN8TOARS
U2 - 10.1007/s11856-016-1336-3
DO - 10.1007/s11856-016-1336-3
M3 - Article
SN - 0021-2172
VL - 214
SP - 443
EP - 462
JO - Israel Journal of Mathematics
JF - Israel Journal of Mathematics
ER -