Embedding problems related to asymptotic dimension in coarse geometry

2015 Fiscal Year Final Research Report

• Project/Area Number: 24540099
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Geometry
• Research Institution: Waseda University
• Principal Investigator: Koyama Akira 早稲田大学, 理工学術院, 教授 (40116158)
• Co-Investigator(Kenkyū-buntansha): EDA Katsuya 早稲田大学, 理工学術院, 教授 (90015826)
• Co-Investigator(Renkei-kenkyūsha): CHINEN Naotsugu 防衛大学校, 教授 (20370067) ; HOSAKA Tetsuya 静岡大学, 総合科学技術研究科, 准教授 (50344908) ; YAGASAKI Tatsuhiko 京都工芸繊維大学, 工芸科学研究科, 教授 (40191077)
• Project Period (FY): 2012-04-01 – 2016-03-31
• Keywords: 位相幾何学 / 幾何学的トポロジー / coarse幾何学 / asymptotic次元論 / 埋蔵問題

Outline of Final Research Achievements

We investigated large scale geometry, mainly coarse geometry for general proper metric spaces with coarse geometry structure and embedding problems of CAT(0)-groups into the Hilbert space. Then we discovered a good relation between coarse geometry and small scale geometry which is an ordinal geometric topology. I obtained many interesting results with the collaborators, Jozef Kransinkiewicz and Stanislaw Spiez (the Institute of Mathematic, Polish Academy of Science). Our papers have excellent evaluation and we were invited important international conferences of geometric topology. For example, Dubrovnik VIII-Geometric Group Theory and Dynamical Systems, Dubrovnik, Croatia. It is one of traditional and important topology conferences.
Due to our proposal we organized an international meeting of coarse geometry at Wasoeda University. The future speakers are Jerzy Dydak (University of Tennessee, USA)and Stanislaw Spiez. It was a good occasion to exchange hot results and opinions.

Free Research Field

数学