Families of blowups of the real affine plane: Classification, isotopies and visualization

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).