The geometric structures of 3-manifolds and the asymptotic behavior of the Reidemeister torsion for linear representations

• Project/Area Number: 26800030
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: Geometry
• Research Institution: Akita University
• Principal Investigator: Yamaguchi Yoshikazu 秋田大学, 教育文化学部, 准教授 (30534044)
• Project Period (FY): 2014-04-01 – 2017-03-31
• Project Status: Completed (Fiscal Year 2016)
• Budget Amount: ¥3,640,000 (Direct Cost: ¥2,800,000、Indirect Cost: ¥840,000); Fiscal Year 2016: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000); Fiscal Year 2015: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000); Fiscal Year 2014: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
• Keywords: トポロジー / 三次元多様体 / ザイフェルト多様体 / ライデマイスタートーション / 基本群 / 線形表現 / 漸近挙動 / オービフォールド / 幾何構造 / オイラー標数 / ザイフェルト構造 / 双曲構造 / 位相不変量 / 増大度

Outline of Final Research Achievements

The geometric structures of 3-manifolds can be classified into the hyperbolic structures and the Seifert structures. This study has focused on 3-manifolds called Seifert manifolds, which admit Seifert structures, and determined the growth order of the asymptotic behavior of the higher-dimensional Reidemeister torsions and the limits of leading coefficients. Moreover the geometric meaning of the limit of leading coefficient was revealed. These results were derived from the explicit descriptions of the higher-dimensional Reidemeister torsions for Seifert manifolds.

Research Products

• [Int'l Joint Research] The University of Texas at Dallas(米国)
• [Journal Article] A surgery formula for the asymptotics of the higher-dimensional Reidemeister torsion and Seifert fibered spaces (2017)
  • Author(s): Yoshikazu Yamaguchi
  • Journal Title: Indiana University Mathematics Journal Volume: 66
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] The asymptotics of the higher dimensional Reidemeister torsion for exceptional surgeries along twist knots (2017)
  • Author(s): Anh T. Tran and Yoshikazu Yamaguchi
  • Journal Title: Canadian Mathematical Bulletin Volume: 印刷中 Issue: 1 Pages: 211-224
  • DOI: 10.4153/cmb-2017-021-5
  • Peer Reviewed / Int'l Joint Research / Acknowledgement Compliant
• [Journal Article] Twisted Alexander polynomials, character varieties and Reidemeister torsions of double branched covers (2016)
  • Author(s): Yoshikazu Yamaguchi
  • Journal Title: Topology and its applications Volume: 204 Pages: 278-305
  • DOI: 10.1016/j.topol.2016.03.021
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] A surgery formula for the asymptotics of higher dimensional Reidemeister torsion and Seifert fibered spaces (2016)
  • Author(s): Yoshikazu Yamaguchi
  • Journal Title: Indiana University Mathematics Journal Volume: 未定
  • Peer Reviewed / Acknowledgement Compliant
• [Presentation] Reidemeister torsion and exceptional surgeries along the figure eight knot (2016)
  • Author(s): 山口 祥司
  • Organizer: 研究集会「Branched Coverings, Degenerations, and Related Topics 2016」
  • Place of Presentation: 広島大学
  • Year and Date: 2016-03-08
  • Int'l Joint Research / Invited
• [Presentation] Asymptotic behavior of Reidmeister torsion for toroidal surgeries along twist knots (2016)
  • Author(s): 山口 祥司
  • Organizer: 日本数学会トポロジー分科会一般講演
  • Place of Presentation: 関西大学千里山キャンパス
• [Presentation] On the asymptotic behavior of the Reidemeister torsion for toroidal surgeries along twist knots (2016)
  • Author(s): Yoshikazu Yamaguchi
  • Organizer: 国際研究集会「Topology and Geometry of Low-dimensional Manifolds」
  • Place of Presentation: 奈良女子大学
  • Int'l Joint Research / Invited
• [Presentation] On the Reidemeister torsion and toroidal surgeries along the figure eight knot (2015)
  • Author(s): 山口 祥司
  • Organizer: 東北結び目セミナー2015
  • Place of Presentation: 霞城セントラル（山形市）
  • Year and Date: 2015-10-23
• [Presentation] The asymptotics of the Reidemeister torsion for Seifert manifolds and PSL(2, R)-representations of Fuchsian groups (2015)
  • Author(s): 山口 祥司
  • Organizer: 日本数学会トポロジー分科会一般講演
  • Place of Presentation: 明治大学駿河台キャンパス
  • Year and Date: 2015-03-23
• [Presentation] Quantum Topology and Physics 2014 in Fukuoka (2014)
  • Author(s): 山口 祥司
  • Organizer: The asymptotics of the Reidemeister torsion for a Seifert manifold and SL(2,R)-representations
  • Place of Presentation: 九州大学西新プラザ
  • Year and Date: 2014-09-20
  • Invited