Applications to the higher category theory and the field with one element to the stable homotopy theory

2014 Fiscal Year Final Research Report

• Project/Area Number: 23540084
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Geometry
• Research Institution: Nagoya Institute of Technology
• Principal Investigator: MINAMI Norihiko 名古屋工業大学, 工学(系)研究科(研究院), 教授 (80166090)
• Project Period (FY): 2011-04-28 – 2015-03-31
• Keywords: 高次圏 / ホモトピー論 / 一元体 / 代数的K理論 / トポロジカル絶縁体

Outline of Final Research Achievements

An article of elementary number theory, which emphasized view points of the F_1-schemes (or the field with one element), was published in the journal of Number Theory.
As I picked up my level of understanding of the Morel-Voevodsky paper of the A^1-homotopy thoery, I publised its survey paper in the RIMS Kokyuroku Bessatsu. While I got intersted in apparent completely unrelated suubjects of the Bockstedt-Hsiang-Madsen algebraic K analogue of the Novikov conjecture and the topological insulators with disorder, I realized the Baum-Connes conjecture of he noncommutative geometry is a common place to be explored for bot of these researches.

Free Research Field

Homotopy Theory