Homotopically trivial symmetries of Haken manifolds are toral

Michael Freedman Shing-Tung Yau

Geometric Analysis and Geometric Topology mathscidoc:1912.43607

Topology, 22, (2), 179-189, 1983.1
WE CONSIDER Haken manifolds M. That is three manifolds which are compact, irreducible, orientable, and sufficiently 1arge. S 8M may or may not be empty. This class of 3-manifolds shares many properties with closed surfaces (# S2 or RP2). On an algebraic level, both are examples of K (T, 1)s. More geometrically the hierarchy structure of a Haken manifold [9] is analogous to a sequence of cuts turning a surface into a disk. With the aid of minimal surfaces we are able to find a sufficiently natural hierarchy to establish a new similarity between Haken manifolds and surfaces. Our main theorem is:
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  title={Homotopically trivial symmetries of Haken manifolds are toral},
  author={Michael Freedman, and Shing-Tung Yau},
Michael Freedman, and Shing-Tung Yau. Homotopically trivial symmetries of Haken manifolds are toral. 1983. Vol. 22. In Topology. pp.179-189. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224204403768633171.
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