Cheeger Constants of Two Related Hyperbolic Riemann Surfaces

Student thesis: Master's ThesisMaster of Arts (MA)

Abstract

This thesis concerns the study of the Cheeger constant of two related hyperbolic Riemann surfaces. The first surface R is formed by taking the quotient U2/Γ(4), where U2 is the upper half-plane model of the hyperbolic plane and Γ(4) is a congruence subgroup of PSL2(Z), an isometry group of U2 . This quotient is shown to form a Riemann surface which is constructed by gluing sides of a fundamental domain for Γ(4) together according to certain specified side pairings. To form the related Riemann surface R' , we follow a similar procedure, this time taking the quotient U2/G, where G is an index 2 subgroup of Γ(4). For both R and R' , we provide an estimate of the Cheeger constant using a procedure given in [2]. The Cheeger constant is believed to be the same for both surfaces.
Date of Award2021
Original languageAmerican English
Awarding Institution
  • Eastern Illinois University
SupervisorGrant Lakeland (Supervisor)

ASJC Scopus Subject Areas

  • Geometry and Topology

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