Differential Geometry and Topology

course: Deformations and global smoothing of topological calibrations, Calabi-Yau, HyperKaehler, G2, Spin(7) structures

speaker: Ryushi Goto (Osaka University)

abstract: In this talk, I shall focus on geometric structures defined by closed differential forms and develop a systematic approach of the deformation problem of these structures. Introducing suitable cohomology groups, I establish a criterion of unobstructed deformations from the cohomological point of view. Then as an application, I obtain a unified construction of moduli spaces of Calabi-Yau, HyperKaehler, G₂ and Spin(7) structures.

I also apply this approach to certain geometric structures on complex solvable manifolds, which are quotients of solvable Lie groups by discrete subgroups.

Finally, I discuss the problem as to when geometric structures with singularities can be deformed to be smooth ones. I show that the vanishing of certain cohomology classes with compact support is crucial to the smoothing problem.

The talk will be based on the paper Moduli spaces of topological calibrations, International J. Math. 15 (2004), 211-257

timetable:
Wed 22 Sep, 15:30 - 17:00, Sala Conferenze Centro De Giorgi
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