Cusp closing of hyperbolic manifolds
Tóm tắt
A general method to produce infinitely many pairwise homotopically nonequivalent closed manifolds using the cusp closing construction is presented. An infinite sequence of closed homotopically nonequivalent real analytic Riemannian 5-manifolds with uniformly bounded volumes and uniformly bounded nonpositive sectional curvatures, which are allowed to vanish along codimension two submanifolds only, is constructed using this method.
Tài liệu tham khảo
Dold, A.: Lectures on Algebraic Topology, Springer-Verlag, Berlin, 1972.
Gromov, M.: Manifolds of negative curvature, J. Differential Geom. 13 (1978), 223–230.
Gromov, M.: Asymptotic invariants of infinite groups, Preprint IHES, 1992.
Thurston, W.: The geometry and topology of 3-manifolds, Lecture Notes, Princeton Univ., 1977/78.
Schroeder, V.: A cusp closing theorem, Proc. Amer. Math. Soc. 106 (1989), 797–802.