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Lie Groups and Representation Theory
Seminar information archive ～04/28｜Next seminar｜Future seminars 04/29～
| Date, time & place | Tuesday 16:30 - 18:00 126Room #126 (Graduate School of Math. Sci. Bldg.) |
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2026/05/19
17:30-18:30 Room #056 (Graduate School of Math. Sci. Bldg.)
Joint with Tuesday Seminar on Topology.
Yosuke Morita (Kyushu University)
Compact Clifford-Klein forms and homotopy theory of sphere bundles (Japanese)
Joint with Tuesday Seminar on Topology.
Yosuke Morita (Kyushu University)
Compact Clifford-Klein forms and homotopy theory of sphere bundles (Japanese)
[ Abstract ]
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.
