A study on the relationship between invariants of homology cylinders, and its applications
| 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
|
| Project Status |
Completed (Fiscal Year 2014)
|
| Budget Amount *help |
¥4,030,000 (Direct Cost: ¥3,100,000、Indirect Cost: ¥930,000)
Fiscal Year 2014: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2013: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2012: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
|
|---|
| 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 / アレキサンダー多項式 / 写像類群 |
|---|
| 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.
|
Report
(4 results)
Research Products
(9 results)
