Comprehensive studies on topology, analysis and geometry of singular spaces and related topics

2014 Fiscal Year Final Research Report

• Project/Area Number: 24540085
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Geometry
• Research Institution: Kagoshima University
• Principal Investigator: YOKURA Shoji 鹿児島大学, 理工学研究科, 教授 (60182680)
• Co-Investigator(Kenkyū-buntansha): MIYAJIMA Kimio 鹿児島大学, 大学院理工学研究科, 教授 (40107850) ; AIKOU Tadashi 鹿児島大学, 大学院理工学研究科, 教授 (00192831) ; NAKAOKA Hiroyuki 鹿児島大学, 大学院理工学研究科, 准教授 (90568677)
• Co-Investigator(Renkei-kenkyūsha): OHMOTO Toru 北海道大学, 大学院理学研究科, 教授 (20264400) ; YASUDA Takehiko 大阪大学, 大学院理学研究科, 准教授 (30507166)
• Project Period (FY): 2012-04-01 – 2015-03-31
• Keywords: 特異多様体 / 相対Grothendieck群 / motivic 特性類 / algebraic cobordism / bivariant theory / fiberwise bordism group / Donaldson-Thomas不変量

Outline of Final Research Achievements

(1) We have constructed a bivariant-theoretic version of the natural transformation T_y_*:K_0(V/X) ->H_*(X, Q[y]) and Donaldson-Thomas type transformations of the natural transformation T_y_ * (the results were published in Advances in Mathematics and Journal of Singularities, respectivley). (2) We have considered the natural transformation T_y_ * on the symmetric product of spaces ( the results will be published in Crelles Journal (Journal fuer die reine und angewandte Mathematik)). (3) We constructed Oriented Bivariant Theory as a prototype of a bivariant theoretic version of Algebraic Cobordism of Levine-Morel-Pandharipande, and we introduced the notion of fiberwise bordism, motivated by or hinted by the method of constructing the Oriented Bivariant Theory and we constructed a bivariant analogue of the fiberwise bordism.

Free Research Field

topology, algebraic geometry