Geometry and Topology Seminar—— A Generalization of Seifert Geometry Based on the Siegel Upper Half-Space
报告人：蓝青（304am永利集团）
时间：2025-03-26 15:10-17:00
地点：智华楼四元厅
【摘要】
The $\widetilde{\mathrm{SL}(2,\mathbb{R})}$-geometry is one of Thurston's eight geometries, which fibers over the hyperbolic plane. Generalizing this geometry, we construct a geometry fibering over the Siegel upper half-space, and provide a volume formula for some manifolds with this geometry.
For $n=2$, a prototype is first constructed via the normal bundle of an equivariant embedding into a Grassmannian manifold. It turns out that this geometry is the homogeneous space given by a central extension of $\widetilde{\mathrm{Sp}(2n,\mathbb{R})}$, modulo its maximal compact subgroup. After fixing a convention for the invariant measure, the volume of a ``Seifert-like'' closed manifold of this geometry is given by the length of the fiber circle times the Euler characteristic of the base manifold, up to a sign.
