Nonzero degree maps between three dimensional manifolds
Institution: | University of California – Berkeley |
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Department: | Mathematics |
Year: | 2012 |
Keywords: | Mathematics; 3-manifolds; nonzero degree maps |
Record ID: | 1976362 |
Full text PDF: | http://www.escholarship.org/uc/item/0jj5791w |
The main result of this dissertation shows that every orientable closed 3-manifold admits a nonzero degree map onto at most finitely many homeomorphically distinct non-geometric prime 3-manifolds. Furthermore, for any integer <italic>d</italic> > 0, every orientable closed 3-manifold admits a map of degree <italic>d</italic> onto only finitely many homeomorphically distinct 3-manifolds. This answers a question of Yongwu Rong. The finiteness of JSJ piece of the targets under nonzero degree maps was known earlier by the results of Soma and Boileau–Rubinstein–Wang, and a new proof is provided is this dissertation. We also prove analogous results for dominations rela-tive to boundary. As an application, we describe the degree set of dominations onto integral homology 3-spheres.