Infinitely generated objects (1-2 dimensional wild spaces and fundamental groups)

2015 Fiscal Year Final Research Report

• Project/Area Number: 23540110
• 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: Eda Katsuya 早稲田大学, 理工学術院, 教授 (90015826)
• Project Period (FY): 2011-04-28 – 2015-03-31
• Keywords: fundamental group / wild spaces / one dimensional / two dimensional / Peano continua / singular homology group / topological group / grope group

Outline of Final Research Achievements

We studied on the subjects (1) 2 dimensional nonaspherical cell-like continua [2,3]; (2) The inverse limits of finitely generated free groups [4]; (3) Grope groups [5] (4) Covering maps over topological groups [6]; (5) Singular homology groups of one-dimensional Peano continua [1].

(1) We propose four constructions of spaces which produce 2 dimensional nonaspherical cell-like continua. There exists a Peano continuum for each two of them which shows the difference of the two constructions. (2) The inverse limits of inverse sequences of free groups of finite rank are free groups of finite rank or four non-isomrphic groups. (3) If there exists a nontrivial homomorphism from the minimal grope group to another grope group, then the grope has a binary braching part as the minimal grope. (4) There exist infinite sheeted covering maps over any solenoids. (5) Singular homology groups of one-dimensional Peano continua are free abelian groups of finite rank or that of the Hawaiian earring.

Free Research Field

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