A study on the relationship between invariants of homology cylinders, and its applications

2014 Fiscal Year Final Research Report

• Project/Area Number: 24540068
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Geometry
• Research Institution: Tokyo University of Agriculture and Technology
• Principal Investigator: GODA HIROSHI 東京農工大学, 工学(系)研究科(研究院), 教授 (60266913)
• Co-Investigator(Renkei-kenkyūsha): SAKASAI Takuya 東京大学, 大学院数理科学研究科, 准教授 (60451902)
• Project Period (FY): 2012-04-01 – 2015-03-31
• Keywords: ホモロジーシリンダー / ファイバー結び目 / 写像類 / モノドロミー

Outline of Final Research Achievements

We focused on 2-bridge fibered knots, whose family is a subset of homologically fibered knots. Then, we obtained a formula of a presentation of its monodromy map as an element in Automorphism of free groups. Using this formula, we gave a formula of the Alexander polynomial. We made a table of elements in Automorphism of free groups, which shows the monodromy maps of homologically fibered 2-bridge knots up to 12 crossings.

Free Research Field

数物系科学，数学，幾何学