Date of Graduation

5-2020

Document Type

Dissertation

Degree Name

Doctor of Philosophy in Mathematics (PhD)

Degree Level

Graduate

Department

Mathematical Sciences

Advisor/Mentor

Rieck, Yo’av

Committee Member

Goodman-Strauss, Chaim

Second Committee Member

Clay, Matthew

Keywords

Manifolds; Orbifolds; Topology

Abstract

We explicitly construct 10 families of bad 3-orbifolds, X , having the following property: given any bad 3-orbifold, O, it admits an embedded suborbifold X ∈ X such that after removing this member from O, and capping the resulting boundary, and then iterating this process finitely many times, you obtain a good 3-orbifold. Reversing this process gives us a procedure to obtain any possible bad 3-orbifold starting with a good 3-orbifold. Each member of X has 1 or 2 spherical boundary components and has underlying topological space S2 × I or (S2 × S1)\B3.

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