Multiplicity of a space over another space

2017 Fiscal Year Final Research Report

• Project/Area Number: 15K13439
• Research Category: Grant-in-Aid for Challenging Exploratory Research
• Allocation Type: Multi-year Fund
• Research Field: Geometry
• Research Institution: Waseda University
• Principal Investigator: Taniyama Kouki 早稲田大学, 教育・総合科学学術院, 教授 (10247207)
• Project Period (FY): 2015-04-01 – 2018-03-31
• Keywords: 多重度 / 結び目 / 空間グラフ

Outline of Final Research Achievements

Let $(X,\cdot)$ be a magma. A map $a:{\mathbb Z}\to X$ is a right-recursive sequence if $a(n)\cdot a(n+1)=a(n+2)$ for every $n\in{\mathbb Z}$. A map $a:{\mathbb Z}\to X$ is a left-recursive sequence if $a(n+2)=a(n+1)\cdot a(n)$ for every $n\in{\mathbb Z}$. When $(X,\cdot)=({\mathbb Z},+)$ a right-recursive sequence is a left-recursive sequence and it is a Fibonacci type sequence defined on ${\mathbb Z}$. We study various right-recursive sequences and left-recursive sequences. We also study various surjective right-recursive sequences and left-recursive sequences.

Free Research Field

幾何学