Date of Award
2017
Document Type
Honors Thesis (Open Access)
Department
Colby College. Mathematics and Statistics Dept.
Advisor(s)
Dr. Scott A. Taylor
Abstract
Chirality (or handedness) is the property that a structure is “different” from its mirror image. Topology can be used to provide a rigorous framework for the notion of chirality. This project examines various types of chirality and discusses tools to detect chirality in graphs and knots. Notable theorems that are discussed in this work include ones that identify chirality using properties of link polynomials (HOMFLY polynomials), rigid vertex graphs, and knot linking numbers. Various other issues of chirality are explored, and some specially unique structures are discussed. This paper is borne out of reading Dr. Erica Flapan’s book, When Topology Meets Chemistry. It follows the structure of the book closely, and in a sense, tells the same story, but as a modern adaptation. Every uncited theorem and definition and fact is from this book.
The second part of this work focuses on using graph theory to better span molecular graphs. This part is significantly less explored, but nevertheless, presents some interesting prospects.
Keywords
topology, chemistry, chirality, knot theory, graph theory
Recommended Citation
Hardikar, Tarini S., "Tying the Knot: Applications of Topology to Chemistry" (2017). Honors Theses. Paper 857.https://digitalcommons.colby.edu/honorstheses/857