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Lie群論・表現論セミナー
過去の記録 ～04/29｜次回の予定｜今後の予定 04/30～
| 開催情報 | 火曜日 16:30～18:00 数理科学研究科棟(駒場) 126号室 |
|---|---|
| 担当者 | 小林俊行 |
| セミナーURL | https://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar.html |
2026年05月19日(火)
17:30-18:30 数理科学研究科棟(駒場) 056号室
トポロジー火曜セミナーと合同開催。
森田陽介 氏 (九州大学)
Compact Clifford-Klein forms and homotopy theory of sphere bundles (Japanese)
トポロジー火曜セミナーと合同開催。
森田陽介 氏 (九州大学)
Compact Clifford-Klein forms and homotopy theory of sphere bundles (Japanese)
[ 講演概要 ]
Let G/H be a homogeneous space of reductive type (such as the pseudo-Riemannian hyperbolic space H^{p,q}). If a discrete subgroup of G acts properly and freely on G/H, the quotient space becomes a manifold locally modelled on G/H and is called a Clifford-Klein form. In this talk, I will explain a new necessary condition on G/H for the existence of compact Clifford-Klein forms, formulated in terms of homotopy theory of sphere bundles. Our theorem and Adams's solution to the ‘vector fields on sphere’ problem (1962) together imply the following result: unless p is divisible by 2^{ν(q)}, there does not exist a compact complete pseudo-Riemannian manifolds of signature (p,q) with constant negative sectional curvature. Here, ν(q) is an explicit natural number roughly equal to q/2. This is joint work with Fanny Kassel and Nicolas Tholozan.
Let G/H be a homogeneous space of reductive type (such as the pseudo-Riemannian hyperbolic space H^{p,q}). If a discrete subgroup of G acts properly and freely on G/H, the quotient space becomes a manifold locally modelled on G/H and is called a Clifford-Klein form. In this talk, I will explain a new necessary condition on G/H for the existence of compact Clifford-Klein forms, formulated in terms of homotopy theory of sphere bundles. Our theorem and Adams's solution to the ‘vector fields on sphere’ problem (1962) together imply the following result: unless p is divisible by 2^{ν(q)}, there does not exist a compact complete pseudo-Riemannian manifolds of signature (p,q) with constant negative sectional curvature. Here, ν(q) is an explicit natural number roughly equal to q/2. This is joint work with Fanny Kassel and Nicolas Tholozan.
