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Dimension of Virtually Cyclic Classifying Spaces for Certain Geometric Groups
Joecken, Kyle

2013, Doctor of Philosophy, Ohio State University, Mathematics.

Given a connected, oriented, closed 3-manifold M, we construct models for EVCΓ, the classifying space of Γ = π1(M) with isotropy in the virtually cyclic subgroups; we also compute the smallest possible geometric dimension for EVCΓ, pointing out in which cases the models are larger than necessary.


This is done by decomposing M using the prime and JSJ decompositions; the resulting manifolds are either closed and geometric or compact with geometric interior by Thurston's Geometrization Conjecture. We develop a pushout construction of models for virtually cyclic classifying spaces of fundamental groups of Seifert fiber spaces with base orbifold modeled on H2, then (using a pushout method of Lafont and Ortiz) we combine these with known models for the remaining pieces to obtain a model for EVCΓ. These models are then analyzed using Bredon cohomology theory to see if they are of the smallest possible dimension.

Jean-Francois Lafont (Advisor)
Nathan Broaddus (Committee Member)
Michael Davis (Committee Member)
Ivonne Ortiz (Committee Member)
117 p.

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Joecken, K. (2013). Dimension of Virtually Cyclic Classifying Spaces for Certain Geometric Groups. (Electronic Thesis or Dissertation). Retrieved from https://etd.ohiolink.edu/

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Joecken, Kyle. "Dimension of Virtually Cyclic Classifying Spaces for Certain Geometric Groups." Electronic Thesis or Dissertation. Ohio State University, 2013. OhioLINK Electronic Theses and Dissertations Center. 25 Sep 2017.

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Joecken, Kyle "Dimension of Virtually Cyclic Classifying Spaces for Certain Geometric Groups." Electronic Thesis or Dissertation. Ohio State University, 2013. https://etd.ohiolink.edu/

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