The Digital Hopf Construction

Authors

Gregory Lupton, Cleveland State UniversityFollow
John F. Oprea, Cleveland State UniversityFollow
Nicholas A. Scoville, Ursinus College

Document Type

Article

Publication Date

3-2023

Publication Title

Topology and Its Applications

Abstract

Various concepts and constructions in homotopy theory have been defined in the digital setting. Although there have been several attempts at a definition of a fibration in the digital setting, robust examples of these digital fibrations are few and far between. In this paper, we develop a digital Hopf fibration within the category of tolerance spaces. By widening our category to that of tolerance spaces, we are able to give a construction of this digital Hopf fibration that mimics the smooth setting.

Comments

This work was partially supported by grants from the Simons Foundation: (#209575 to Gregory Lupton and #244393 to John Oprea).

Repository Citation

Lupton, Gregory; Oprea, John F.; and Scoville, Nicholas A., "The Digital Hopf Construction" (2023). Mathematics and Statistics Faculty Publications. 356.
https://engagedscholarship.csuohio.edu/scimath_facpub/356

DOI

10.1016/j.topol.2022.108405

Volume

326