On Gromov-Witten Invariants, Hurwitz Numbers and Topological Recursion

• Author / Creator

  Anajao, Rosa P

• In this thesis, we present expositions of Gromov-Witten invariants, Hurwitz numbers, topological recursion and their connections. By remodeling theory, open Gromov-Witten invariants of C^3 and C^3/Za satisfy the topological recursion of Eynard-Orantin defined on framed mirror curve of toric Calabi-Yau three orbifold target spaces. Studies show that simple/orbifold Hurwitz numbers can be obtained using topological recursion with spectral curve given by Lambert/a-Lambert curve. Also, both the open Gromov-Witten invariants of toric Calabi-Yau three orbifold and the simple and double Hurwitz numbers can be formulated via Hodge integrals. We extend these connections by determining the relationship between the open Gromov-Witten invariants of C^3/Za (with insertions of orbifold cohomology classes) and the full double Hurwitz numbers through referring to their Hodge integral formulations and to orbifold Riemann-Roch formula. By remodeling theory and mirror theorem for disk potentials, we make a conjecture relating a specific type of double Hurwitz
  numbers Hg(ν(γ, 2), μ) and topological recursion. We predict that these double Hurwitz numbers Hg(ν(γ, 2), μ) can be generated using topological recursion defined on the spectral curve ye^{−2y} − τxe^{−y} + x^2 = 0.

• Subjects / Keywords

  • Hurwitz Numbers
  • Topological Recursion
  • Gromov-Witten Invariants
  • Mathematical Physics

• Graduation date

  Fall 2015

• Type of Item

  Thesis

• Degree

  Master of Science

• DOI

  https://doi.org/10.7939/R33X83R3P

• License

  This thesis is made available by the University of Alberta Libraries with permission of the copyright owner solely for non-commercial purposes. This thesis, or any portion thereof, may not otherwise be copied or reproduced without the written consent of the copyright owner, except to the extent permitted by Canadian copyright law.