TY - JOUR
T1 - Taut foliations
AU - Colin, Vincent
AU - Kazez, William H.
AU - Roberts, Rachel
N1 - Publisher Copyright:
© 2019 International Press of Boston, Inc.. All rights reserved.
PY - 2019
Y1 - 2019
N2 - We describe notions of tautness that arise in the study of C0 foliations, C1;0 or smoother foliations, and in geometry. We give examples to show that these notions are different. We prove that these variations of tautness are equivalent up to topological conjugacy, but their differences impact some classical foliation results. In particular, we construct examples of smoothly taut C∞;0 foliations that can be C0 approximated by both weakly symplectically fillable, universally tight contact structures and by overtwisted contact structures.
AB - We describe notions of tautness that arise in the study of C0 foliations, C1;0 or smoother foliations, and in geometry. We give examples to show that these notions are different. We prove that these variations of tautness are equivalent up to topological conjugacy, but their differences impact some classical foliation results. In particular, we construct examples of smoothly taut C∞;0 foliations that can be C0 approximated by both weakly symplectically fillable, universally tight contact structures and by overtwisted contact structures.
UR - https://www.scopus.com/pages/publications/85072220333
U2 - 10.4310/cag.2019.v27.n2.a4
DO - 10.4310/cag.2019.v27.n2.a4
M3 - Article
AN - SCOPUS:85072220333
SN - 1019-8385
VL - 27
SP - 357
EP - 375
JO - Communications in Analysis and Geometry
JF - Communications in Analysis and Geometry
IS - 2
ER -