Periodic Pieces of Pseudo-Anosov Flows in Graph Manifolds

• Other Authors: Waller, Russell L. (authoraut)
• Format: Others
• Language: English; English
• Published: Florida State University
• Subjects: Mathematics
• Online Access: http://purl.flvc.org/fsu/fd/FSU_migr_etd-9479

Our work builds on that of Barbot and Fenley to generalize Bonatti and Langevin's famous construction of a graph manifold with pseudo-Anosov flow in which all Seiftert fibered pieces of the torus decomposition are periodic. We provide infinitely many new examples of such graph manifolds, as well as a complete classification -- up to Seifert invariant -- in the case that each Seiftert fibered piece is orientable and the flow is Anosov. We further demonstrate that the singularities of the flow are not rigid but can rather be "rearranged", or even removed, without affecting the ambient manifold. To build our graph manifolds and model the pseudo-Anosov flows that they support, we define and construct combinatorial objects known as flow graphs. We study these flow graphs and the surfaces, called fat graphs (or ribbon graphs), that retract onto them. In particular, we study flow graphs with the additional conditions needed to generate pseudo-Anosov flows from the combinatorial data that the flow graphs provide, and classify the surfaces that admit flow graphs with these additional requirements. === A Dissertation submitted to the Department of Mathematics in partial fulfillment of the requirements for the degree of Doctor of Philosophy. === Spring Semester, 2015. === March 18, 2015. === fat graph, graph manifold, pseudo-Anosov flow, ribbon graph === Includes bibliographical references. === Sergio Fenley, Professor Directing Dissertation; Laura Reina, University Representative; Eriko Hironaka, Committee Member; Wolfgang Heil, Committee Member; Washington Mio, Committee Member.