TL;DR
This paper reviews the topological model of quaternions and extends it to develop a new topological model for octonions, highlighting their non-associative structure.
Contribution
It introduces a novel topological model for octonions based on the Dirac string trick, expanding the geometric understanding of these algebraic structures.
Findings
Developed a topological model for octonions
Extended the Dirac string trick to non-associative structures
Provided insights into the geometric nature of octonions
Abstract
In this paper we review the topological model for the quaternions based upon the Dirac string trick. We then extend this model, to create a model for the octonions - the non-associative generalization of the quaternions.
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Taxonomy
TopicsAlgebraic and Geometric Analysis