کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
5777973 | 1633056 | 2017 | 17 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Sphere eversion from the viewpoint of generic homotopy
ترجمه فارسی عنوان
انحراف از دیدگاه ژنومیک هومیوپاتی
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موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
هندسه و توپولوژی
چکیده انگلیسی
In 1958, Smale proved that any immersions of S2 to R3 are regularly homotopic. This means that we can turn an embedded sphere in R3 inside out by a regular homotopy. After Smale showed his result without visualization, many people visualized sphere eversions, in various ways. In this paper, we construct a sphere eversion by lifting a “simple” generic homotopy of S2 to R2 to a generic regular homotopy of S2 to R3. By doing so, our eversion is simple in terms of deformation of the contour generators of immersed spheres. We also visualize the 3-dimensional interlinking of the contour generators and the self-intersections of each stage of immersed spheres.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Topology and its Applications - Volume 223, 1 June 2017, Pages 13-29
Journal: Topology and its Applications - Volume 223, 1 June 2017, Pages 13-29
نویسندگان
Mikami Hirasawa, Minoru Yamamoto,