BLACK HOLES IN THE DYNNIKOV COORDINATE PLANE

BLACK HOLES IN THE DYNNIKOV COORDINATE PLANE | Authorea try { document.documentElement.classList.add('js'); } catch (e) { } var _gaq = _gaq || []; _gaq.push(['_setAccount', 'G-8VDV14Y67G']); _gaq.push(['_trackPageview']); (function() { var ga = document.createElement('script'); ga.type = 'text/javascript'; ga.async = true; ga.src = ('https:' == document.location.protocol ? 'https://ssl' : 'http://www') + '.google-analytics.com/ga.js'; var s = document.getElementsByTagName('script')[0]; s.parentNode.insertBefore(ga, s); })(); Skip to main content Preprints Collections Wiley Open Research IET Open Research Ecological Society of Japan All Collections About About Authorea FAQs Contact Us Quick Search anywhere Search for preprint articles, keywords, etc. Search Search ADVANCED SEARCH SCROLL This is a preprint and has not been peer reviewed. Data may be preliminary. 11 April 2025 V1 Latest version Share on BLACK HOLES IN THE DYNNIKOV COORDINATE PLANE Author : FERIHE ATALAN 0000-0001-6547-0570 [email protected] Authors Info & Affiliations https://doi.org/10.22541/au.174434772.20639079/v1 133 views 70 downloads Contents Abstract Supplementary Material Information & Authors Metrics & Citations View Options References Figures Tables Media Share Abstract We study the dynamics of Dehn twists acting on the Dynnikov coordinate plane associated with a thrice-punctured disc. This action, arising from the pure mapping class group, is shown to be piecewise-linear and area-preserving. We describe invariant regions under iteration---termed "black holes"---and present algorithms to compute distances in the curve complex and to track the action of pseudo-Anosov maps. Our results offer new geometric interpretations and reveal structural parallels with toric surfaces and higher-genus covers. Supplementary Material File (fa_black_holes.pdf) Download 446.25 KB Information & Authors Information Version history V1 Version 1 11 April 2025 Copyright This work is licensed under a Non Exclusive No Reuse License. Keywords dehn twists dynnikov coordinates free groups mapping class groups Authors Affiliations FERIHE ATALAN 0000-0001-6547-0570 [email protected] Atilim Universitesi View all articles by this author Metrics & Citations Metrics Article Usage 133 views 70 downloads .FvxKWukQNSOunydq8rnd { width: 100px; } Citations Download citation FERIHE ATALAN. BLACK HOLES IN THE DYNNIKOV COORDINATE PLANE. Authorea . 11 April 2025. DOI: https://doi.org/10.22541/au.174434772.20639079/v1 If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download. For more information or tips please see 'Downloading to a citation manager' in the Help menu . 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