GEOMETRIZATION OF DEHN TWIST TORI OF A SURFACE WITH INFINITE GENUS


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Abstract

The conditions under which an infinite three-dimensional graph manifold M carries a metric of nonpositive bounded curvature (an NPC-metric) having finite volume are studied. A complete list of all such manifolds is obtained in the case where M is the mapping torus of a collection of Dehn twists on a surface of infinite genus and the graph of M is linear (i.e., homeomorphic to a line or a ray). Bibliography: 4 titles.

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