Families of blowups of the real affine plane: Classification, isotopies and visualization. (May 2021)

• Record Type: Journal Article
• Authors: Brodmann, Markus; Schenzel, Peter
• Is Part Of: Journal of symbolic computation. Volume 104(2021)
• Page Start: 874
• Page End: 898
• Publication Date: 2021-05
• Subjects: primary 14E07 14P25 -- secondary 14R05 13P99; Embedded blowup -- Embedded isomorphism -- Embedded isotopy -- Connecting family; Mathematics -- Data processing -- Periodicals; Numerical analysis -- Data processing -- Periodicals; Automatic programming (Computer science) -- Periodicals; Mathématiques -- Informatique -- Périodiques; Analyse numérique -- Informatique -- Périodiques; Programmation automatique -- Périodiques; Automatic programming (Computer science); Mathematics -- Data processing; Numerical analysis -- Data processing; Periodicals; Electronic journals; 510.285
• DOI: 10.1016/j.jsc.2020.10.004
• Languages: English
• ISSNs: 0747-7171

Abstract

Abstract: We classify embedded blowups of the real affine plane up to oriented isomorphy. We show that two blowups in the same isomorphism class are isotopic, using a matrix deformation argument similar to an idea given in Shastri (2002) . This answers two questions which were motivated by the interactive visualizations of such blowups (see Schenzel and Stussak, 2013, Stussak, 2007, 2013 ).