Foliations on three dimensional manifolds

• Project/Area Number: 21740055
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Single-year Grants
• Research Field: Geometry
• Research Institution: Nara Women's University
• Principal Investigator: MURAI Hiroko 奈良女子大学, 理学部, 助教 (40456843)
• Project Period (FY): 2009 – 2011
• Project Status: Completed (Fiscal Year 2011)
• Budget Amount: ¥1,950,000 (Direct Cost: ¥1,500,000、Indirect Cost: ¥450,000); Fiscal Year 2011: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000); Fiscal Year 2010: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000); Fiscal Year 2009: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
• Keywords: 3次元多様体 / Heegaard 分解 / Heegaard 曲面 / 本質的lamination / 結び目 / 葉層構造 / Heegaard分解 / Heegaard曲面 / 計算機

Research Abstract

We studied intersections of essential laminations and Heegaard surfaces which give strongly irreducible Heegaard splittings in three dimensional manifolds. It is known that such Heegaard surfaces intersect essential surfaces in essential simple closed curves. We gave a similar result when Heegaard genus is two. We also gave some examples which give a phenomenon specific to non-compact objects.

Research Products

• [Journal Article] Gap of codimension one foliations (2012)
  • Author(s): H. Murai
  • Journal Title: Kobe Journal of Mathematics Volume: Vol.29 Pages: 1-24
  • Peer Reviewed
• [Presentation] A Haken type theorem on intersections of essential laminations and genus 2 Heegaard surfaces (2011)
  • Author(s): 小林毅、村井紘子
  • Organizer: 九大トポロジー金曜セミナー
  • Place of Presentation: 九州大学伊都キャンパス
  • Year and Date: 2011-07-22
• [Presentation] A Haken type theorem on intersections of essential laminations and genus 2 Heegaard surfaces (2011)
  • Author(s): 小林毅、村井紘子
  • Organizer: Workshop on Topology and Geometry-Heegaard splitting of 3-manifolds--
  • Place of Presentation: 広島大学
  • Year and Date: 2011-06-28
• [Presentation] A Haken type theorem on intersections of essential laminations and genus 2 Heegaard surfaces (2011)
  • Author(s): T. Kobayashi、H. Murai
  • Organizer: Workshop on Low Dimensional Topology in Shanghai and Suzhou
  • Place of Presentation: Suzhou University、China
  • Year and Date: 2011-05-17
• [Presentation] A Haken type theorem on intersections of essential laminations and genus 2 Heegaard surfaces (Joint work with Prof.Tsuyoshi Kobayashi) (2011)
  • Author(s): 村井紘子
  • Organizer: Workshop on Low Dimensional Topology m Shanghai and Suzhou
  • Place of Presentation: 蘇州大学
  • Year and Date: 2011-05-17
• [Presentation] Toward Haken type theorems for essential laminations in 3-manifolds (2011)
  • Author(s): 小林毅、村井紘子
  • Organizer: 東北大学幾何セミナー
  • Place of Presentation: 東北大学
  • Year and Date: 2011-01-18
• [Presentation] Toward Haken type theorems for essential laminations in 3-manifolds : Proposal of fundamental settings and applications (2011)
  • Author(s): 小林毅、村井紘子
  • Organizer: The Seventh East Asian School of Knots and Related Topics
  • Place of Presentation: HAKUWA ホテル、広島
  • Year and Date: 2011-01-11
• [Presentation] A Haken type theorem on intersections of essential laminations and genus 2 Heegaard surfaces L II (joint work in progress with Prof.Tsuyoshi Kobayashi) (2011)
  • Author(s): 村井紘子
  • Organizer: Workshop on Topology and Geometry--Heegaard splitting of 3-manifolds-
  • Place of Presentation: 広島大学
• [Presentation] Toward Haken type theorems for essential laminations in 3-manifolds : Proposal of fundamental settings and applications (2010)
  • Author(s): 小林毅、村井紘子
  • Organizer: E-KOOK セミナー2010
  • Place of Presentation: 大阪市立大学学術情報センター
  • Year and Date: 2010-08-28
• [Presentation] 結び目理論と語のトポロジー理論 (2009)
  • Author(s): 村井紘子
  • Organizer: 2009年度数学・物理学・情報科学の研究交流シンポジウム
  • Place of Presentation: 奈良女子大学
  • Year and Date: 2009-12-19
• [Presentation] Essential laminations and the distance of Heegaard splittings (2009)
  • Author(s): 小 林 毅 、 村井紘子
  • Organizer: 葉層構造と微分同相群研究集会(Foliations and Groups of Diffeomorphisms)
  • Place of Presentation: 東京大学玉原国際セミナーハウス
  • Year and Date: 2009-10-28
• [Presentation] 結び目補空間の葉層構造について (2009)
  • Author(s): 村井紘子
  • Organizer: 大阪市立大学院生談話会
  • Place of Presentation: 大阪市立大学
  • Year and Date: 2009-10-03
• [Presentation] Introduction to essential laminations (2009)
  • Author(s): H. Murai
  • Organizer: 奈良女子大学低次元トポロジー小研究会
  • Place of Presentation: 奈良女子大学
  • Year and Date: 2009-08-17
• [Remarks]
  • URL: http://koto10.nara-wu.ac.jp/Profiles/10/0000903/profile.html