Geometry of secondary characteristic classes

2016 Fiscal Year Final Research Report

• Project/Area Number: 25400083
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Geometry
• Research Institution: Tokyo Institute of Technology
• Principal Investigator: Terashima Yuji 東京工業大学, 情報理工学院, 准教授 (70361764)
• Project Period (FY): 2013-04-01 – 2017-03-31
• Keywords: 微分トポロジー / 特性類 / 数論的トポロジー / ゲージ場の物理 / クラスター変換 / ミューテーション

Outline of Final Research Achievements

We have introduced new quantities called partition q-series for quiver mutation sequences and proved fundamental properties in a joint work with Akishi Kato. One motivation is to provide a solid mathematical foundation to extract essential information of the partition function of a 3-dimensional gauge theory proposed in a joint work with Masahito Yamazaki. In particular, for quivers which are of Dynkin type or square products thereof with special mutation sequences, we have proved that partition q-series are identified with fermionic character formulas of certain modules associated with affine Lie algebras. Moreover, for reddening sequences, we have proved that a graded version of partition q-series essentially coincides with the combinatorial Donaldson-Thomas invariant.

Free Research Field

数物系科学