aspherical manifoldの例文

例文

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1. However, there do exist symplectically aspherical manifolds which are not aspherical spaces.
2. By Stokes'theorem, we see that symplectic manifolds which are aspherical are also symplectically aspherical manifolds.
3. Since aspherical manifolds with isomorphic fundamental groups are homotopy equivalent, the Borel conjecture implies that aspherical closed manifolds are determined, up to homeomorphism, by their fundamental groups.
4. The Borel conjecture is a topological reformulation of Mostow rigidity, weakening the hypothesis from hyperbolic manifolds to aspherical manifolds, and similarly weakening the conclusion from an isometry to a homeomorphism.
5. The Weinstein conjecture was first proved for contact hypersurfaces in \ mathbb R ^ { 2n } in 1986 by Viterbo, then extended to cotangent bundles by Hofer-Viterbo and to wider classes of aspherical manifolds by Floer-Hofer-Viterbo.