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CATEGORIES:Differential Geometry and Topology Seminar
SUMMARY:Homotopy of codimension one foliations on 3-manifo
lds - Helene Eynard\, Jussieu
DTSTART;TZID=Europe/London:20120523T160000
DTEND;TZID=Europe/London:20120523T170000
UID:TALK36665AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/36665
DESCRIPTION:We are interested in the topology of the space of
smooth\ncodimension one foliations on a given clos
ed 3-manifold.\n\nIn 1969\, J. Wood proved that an
y smooth plane field on a closed 3-manifold can be
deformed into a plane field tangent to a foliatio
n. This fundamental result was then reproved and g
eneralized by W. Thurston. It is natural then to w
onder whether two foliations whose tangent plane f
ields are homotopic can be connected by a path of
foliations\, or\, in other words\, if there is act
ually a bijection between the (pathwise)\nconnecte
d components of the space of foliations on a given
manifold and that of the space of plane fields.\n
\nIn this talk\, we will show that the answer is e
ssentially yes. To that end\, we will first presen
t Thurston's construction\, along with later works
by A. Larcanché\, who answered the above question
in the case of two sufficiently close taut foliat
ions.\n
LOCATION:MR13
CONTACT:Ivan Smith
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