Sequences of Pseudo-Anosov Mapping Classes with Asymptotically Small Dilatation

• Other Authors: Valdivia, Aaron David (authoraut)
• Format: Others
• Language: English; English
• Published: Florida State University
• Subjects: Mathematics
• Online Access: http://purl.flvc.org/fsu/fd/FSU_migr_etd-5242

We construct sequences of pseudo-Anosov examples which we use to bound the minimal dilatation on arbitrary surfaces. We show that these bounds give the asymptotic behavior of the minimal dilatations for certain sequences. Further we show that the mapping classes for a given sequence from our construction can be realized as fibrations of a single 3-manifold. === A Dissertation submitted to the Department of Mathematics in partial fulfillment of the requirements for the degree of Doctor of Philosophy. === Fall Semester, 2011. === September 14, 2011. === dilatation, geometric topology, mapping class group, pseudo-Anosov === Includes bibliographical references. === Eriko Hironaka, Professor Directing Dissertation; Laura Reina, University Representative; Wolfgang Heil, Committee Member; Eric Klassen, Committee Member.