Publication Date
8-2025
Date of Final Oral Examination (Defense)
6-20-2025
Type of Culminating Activity
Thesis
Degree Title
Master of Science in Mathematics
Department
Mathematics
Supervisory Committee Chair
Uwe Kaiser, Ph.D.
Supervisory Committee Member
Jens Harlander, Ph.D.
Supervisory Committee Member
Zachariah Teitler, Ph.D.
Abstract
This thesis explores a construction of the family of topological invariants for certain oriented 3-manifolds based on the state-integral approach developed by Andersen, Garoufalidis, and Kashaev in the Archimedean setting. Starting from an ideal triangulation of a 3-manifold equipped with angle data, variables are assigned to the faces and tetrahedra, taking values in a so-called 'Gaussian group'. The invariant is defined by integrating a distribution defined from the combinatorics of the triangulation and a special function over a product of the Gaussian group. The special function is a quantum dilogarithm, whose valuable feature, the pentagon relation, ensures the resulting integral remains unchanged under local modifications of the triangulation, thereby reflecting the topology of the manifold.
DOI
10.18122/td.2403.boisestate
Recommended Citation
Dusenbury, Amelia Palmer, "On the Garoufalidis-Kashaev State-Integral Invariant" (2025). Boise State University Theses and Dissertations. 2403.
10.18122/td.2403.boisestate