Graduation Year

2018

Date of Submission

12-2017

Document Type

Campus Only Senior Thesis

Degree Name

Bachelor of Arts

Department

Mathematics

Reader 1

Sam Nelson

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Terms of Use for work posted in Scholarship@Claremont.

Rights Information

© 2017 Yuqi Zhao

Abstract

This paper focuses on generalizing unoriented handlebody-links to the twisted virtual case, obtaining Reidemeister moves for handlebody-links in ambient spaces. The paper introduces a related algebraic structure known as twisted virtual bikeigebras whose axioms are motivated by the twisted virtual handlebody-link Reidemeister moves. In the research, twisted virtual bikeigebras are used to dene X-colorability for twisted virtual handlebody-links and define an integer-valued invariant of twisted virtual handlebody-links. The paper also includes example computations of the new invariants and use them to distinguish some twisted virtual handlebody-links.

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