Tuesday, July 8, 2025 - 10:15 in U2-147
Geometric structures determined by the 7-sphere
A talk in the Oberseminar Geometric Analysis series by
Sergey Grigorian from University of Texas Rio Grande Valley
| Abstract: |
The 7-sphere is remarkable not only for its rich topological and algebraic properties but also for the special geometric structures it encodes. In this talk, we explore how the symmetries and stabilizer subgroups of Spin(7) acting on the 7-sphere, regarded as the set of unit octonions, give rise to G2-structures on 7-manifolds, SU(3)-structures on 6-manifolds, and SU(2)-structures on 5-manifolds. We will trace how these structures arise naturally via the inclusions of Lie groups and are reflected in the geometry of sphere fibrations. This perspective highlights the role of the 7-sphere as a unifying object in special geometry in dimensions from 5 to 8.
Within the CRC this talk is associated to the project(s): A3 |
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