2012 Fiscal Year Final Research Report

Explicit constructions of secondary characteristic classes

Research Project

Project/Area Number	22740036
Research Category	Grant-in-Aid for Young Scientists (B)
Allocation Type	Single-year Grants
Research Field	Geometry
Research Institution	Tokyo Institute of Technology
Principal Investigator	TERASHIMA Yuji 東京工業大学, 大学院・理工学研究科, 助教 (70361764)
Project Period (FY)	2010 – 2012
Keywords	微分トポロジー特性類
Research Abstract	We have found a new relation of 3-dimensional gauge theory and3-dimensional hyperbolic geometry with Masahito Yamazaki in 2011. We have written a paper on the results. The paper has been published as Y. Terashima and M. Yamazaki, SL(2,R)Chern-Simons, Liouville, and Gauge Theories on Duality Walls, JHEP， 1108, 135. (2011).Following this work, with Masahito Yamazaki, we have found a new relation of indices in4-dimensional gauge theories and hyperbolic volumes of 3-dimensional hyperbolic manifolds with boundary. We have written a paper on the results. The paper has been published as Y. Terashima, M. Yamazaki, Emergent 3-manifolds from four dimensionalsuperconformal indices, Phys. Rev. Lett. ，109, (2012) 091602. This relation suggestsvarious new mathematical results.