• Search Research Projects
  • Search Researchers
  • How to Use
  1. Back to project page

2023 Fiscal Year Final Research Report

Research on the geometric structures of handlebody-knots and their complements

Research Project

  • PDF
Project/Area Number 20K22312
Research Category

Grant-in-Aid for Research Activity Start-up

Allocation TypeMulti-year Fund
Review Section 0201:Algebra, geometry, analysis, applied mathematics,and related fields
Research InstitutionKochi University (2022-2023)
Waseda University (2020-2021)

Principal Investigator

Murao Tomo  高知大学, 教育研究部自然科学系理工学部門, 助教 (10880304)

Project Period (FY) 2020-09-11 – 2024-03-31
Keywords結び目 / ハンドル体結び目 / 空間曲面 / カンドル / ラック / ねじれAlexander不変量 / カンドル(ラック)コサイクル不変量
Outline of Final Research Achievements

We provided a method to construct a pair of maps, called an MCQ Alexander pair, which is used in the construction of f-twisted Alexander invariants of handlebody-knots. Additionally, we organized the algebraic structure of a linear extension of a multiple conjugate quandle and showed a sufficiency of MCQ Alexander pairs in constructing handlebody-knot invariants derived from the linear extensions.
Furthermore, we constructed the (co)homology theory of multiple group racks and the multiple group rack cocycle invariants for oriented spatial surfaces. Using this invariant, we gave examples of classifications of oriented spatial surfaces that cannot be distinguished by classical methods.

Free Research Field

トポロジー

Academic Significance and Societal Importance of the Research Achievements

本研究は,曲面やハンドル体の3次元球面への埋め込まれ方を解明するために,高精度で扱いやすい不変量の構成を目指したものであり,本研究によって得られた成果は結び目理論,低次元多様体論への寄与が期待されるものである.また,具体的な研究結果である,ハンドル体結び目の拡大Alexander不変量に係る多重共役カンドルの代数構造における基礎理論の構築,多重群ラック(コ)ホモロジー理論を用いた空間曲面の分類研究は,今後の研究の基盤となるとともに,研究の方向性を指し示す結果と言える.

URL: 

Published: 2025-01-30  

Information User Guide FAQ News Terms of Use Attribution of KAKENHI

Powered by NII kakenhi