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トポロジー火曜セミナー
過去の記録 ～04/19｜次回の予定｜今後の予定 04/20～
| 開催情報 | 火曜日 17:00～18:30 数理科学研究科棟(駒場) 056号室 |
|---|---|
| 担当者 | 河澄 響矢, 北山 貴裕, 逆井卓也 |
| セミナーURL | http://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index.html |
2010年04月20日(火)
16:30-18:00 数理科学研究科棟(駒場) 056号室
Tea: 16:00 - 16:30 コモンルーム
Helene Eynard-Bontemps 氏 (東京大学大学院数理科学研究科, JSPS)
Homotopy of foliations in dimension 3. (ENGLISH)
Tea: 16:00 - 16:30 コモンルーム
Helene Eynard-Bontemps 氏 (東京大学大学院数理科学研究科, JSPS)
Homotopy of foliations in dimension 3. (ENGLISH)
[ 講演概要 ]
We are interested in the connectedness of the space of
codimension one foliations on a closed 3-manifold. In 1969, J. Wood proved
the fundamental result:
Theorem: Every 2-plane field on a closed 3-manifold is homotopic to a
foliation.
W. R. gave a new proof of (and generalized) this result in 1973 using
local constructions. It is then natural to wonder if two foliations with
homotopic tangent plane fields can be linked by a continuous path of
foliations.
A. Larcanch\\'e gave a positive answer in the particular case of
"sufficiently close" taut foliations. We use the key construction of her
proof (among other tools) to show that this is actually always true,
provided one is not too picky about the regularity of the foliations of
the path:
Theorem: Two C^\\infty foliations with homotopic tangent plane fields can
be linked by a path of C^1 foliations.
We are interested in the connectedness of the space of
codimension one foliations on a closed 3-manifold. In 1969, J. Wood proved
the fundamental result:
Theorem: Every 2-plane field on a closed 3-manifold is homotopic to a
foliation.
W. R. gave a new proof of (and generalized) this result in 1973 using
local constructions. It is then natural to wonder if two foliations with
homotopic tangent plane fields can be linked by a continuous path of
foliations.
A. Larcanch\\'e gave a positive answer in the particular case of
"sufficiently close" taut foliations. We use the key construction of her
proof (among other tools) to show that this is actually always true,
provided one is not too picky about the regularity of the foliations of
the path:
Theorem: Two C^\\infty foliations with homotopic tangent plane fields can
be linked by a path of C^1 foliations.
