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Cohomology fractals, Cannon–Thurston maps, and the geodesic flow
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Bachman, David, Goerner, Matthias, Schleimer, Saul and Segerman, Henry (2022) Cohomology fractals, Cannon–Thurston maps, and the geodesic flow. Experimental Mathematics . pp. 1-39. doi:10.1080/10586458.2021.1994059 ISSN 1944-950X.
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Official URL: https://doi.org/10.1080/10586458.2021.1994059
Abstract
Cohomology fractals are images naturally associated to cohomology classes in hyperbolic three-manifolds. We generate these images for cusped, incomplete, and closed hyperbolic three-manifolds in real-time by ray-tracing to a fixed visual radius. We discovered cohomology fractals while attempting to illustrate Cannon–Thurston maps without using vector graphics; we prove a correspondence between these two, when the cohomology class is dual to a fibration. This allows us to verify our implementations by comparing our images of cohomology fractals to existing pictures of Cannon–Thurston maps.
Item Type: | Journal Article | ||||||
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Subjects: | Q Science > QA Mathematics | ||||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||
SWORD Depositor: | Library Publications Router | ||||||
Library of Congress Subject Headings (LCSH): | Cohomology operations , Fractals , Three-manifolds (Topology), Geometry, Hyperbolic, Geodesic flows | ||||||
Journal or Publication Title: | Experimental Mathematics | ||||||
Publisher: | Informa UK Limited | ||||||
ISSN: | 1944-950X | ||||||
Official Date: | 15 September 2022 | ||||||
Dates: |
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Page Range: | pp. 1-39 | ||||||
DOI: | 10.1080/10586458.2021.1994059 | ||||||
Status: | Peer Reviewed | ||||||
Publication Status: | Published | ||||||
Reuse Statement (publisher, data, author rights): | ** Article version: VoR ** From Crossref journal articles via Jisc Publications Router ** History: epub 15-09-2022; issued 15-09-2022. ** Licence for VoR version of this article starting on 15-09-2022: http://creativecommons.org/licenses/by/4.0/ | ||||||
Access rights to Published version: | Open Access (Creative Commons) | ||||||
Date of first compliant deposit: | 25 October 2022 | ||||||
Date of first compliant Open Access: | 25 October 2022 | ||||||
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