Topological structure of a compactification and its boundary on coarse geometry

2016 Fiscal Year Final Research Report

• Project/Area Number: 25800035
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: Geometry
• Research Institution: Kanagawa University (2016); The University of Tokyo (2013-2015)
• Principal Investigator: MINE Kotaro 神奈川大学, 工学部, 助教 (90512525)
• Project Period (FY): 2013-04-01 – 2017-03-31
• Keywords: Higson境界 / 粗空間 / 大スケール幾何学 / 漸近次元 / 一様空間 / 擬等長 / コンパクト化 / 位相空間

Outline of Final Research Achievements

We studied properties of large scale geometry from a view point of the topology of a boundary at infinity which is called the Higson corona. (1) We investigated a condition of a coarse map on the underlying space which induces a fixed point free homeomorphism on the corona. (2) We discussed a generalization of C_0 structures for uniform spaces and a relation between these Higson compactifications and Smirnov compactifications. (3) We also studied the Higson corona of the product of coarse spaces.

Free Research Field

幾何学的トポロジー