Riemann surfaces and low dimensional manifolds

2017 Fiscal Year Final Research Report

• Project/Area Number: 26400095
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Geometry
• Research Institution: Gakushuin University
• Principal Investigator: Matsumoto Yukio 学習院大学, 理学部, 研究員 (20011637)
• Co-Investigator(Renkei-kenkyūsha): Ashikaga Tadashi 東北学院大学, 工学部, 教授 (90125203) ; Komori Yohei 早稲田大学, 教育総合科学学術院, 教授 (70264794) ; Ohmoto Toru 北海道大学, 理学研究科, 教授 (20264400)
• Project Period (FY): 2014-04-01 – 2018-03-31
• Keywords: リーマン面 / ドリーニュ・マンフォードコンパクト化 / オービフォールド / 結晶群

Outline of Final Research Achievements

It is known that the moduli space of Riemann surfaces admits a natural compactification called the Deligne-Mumford compactification (DM-compactification). The main result of the present research is that we explicitly constructed a "natural" atlas consisting of orbifold charts on the DM-compactification of moduli space. These charts are indexed by the simplices of Harvey's curve complex. As a byproduct of the result, we discovered that certain higher dimensional euclidean crystallographic groups are attached to those orbifold charts that are indexed by the simplices of the maximum dimension. The theoretical meaning of this attachment of crystallographic groups will be studied in the future.

Free Research Field

多様体のトポロジー