کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4650452 1342488 2008 9 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Uniqueness of Walkup's 9-vertex 3-dimensional Klein bottle
کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات ریاضیات گسسته و ترکیبات
پیش نمایش صفحه اول مقاله
Uniqueness of Walkup's 9-vertex 3-dimensional Klein bottle
چکیده انگلیسی

Via a computer search, Altshuler and Steinberg found that there are 1296+11296+1 combinatorial 3-manifolds on nine vertices, of which only one is non-sphere. This exceptional 3-manifold K93 triangulates the twisted S2S2-bundle over S1S1. It was first constructed by Walkup. In this paper, we present a computer-free proof of the uniqueness of this non-sphere combinatorial 3-manifold. As opposed to the computer-generated proof, ours does not require wading through all the 9-vertex 3-spheres. As a preliminary result, we also show that any 9-vertex combinatorial 3-manifold is equivalent by proper bistellar moves to a 9-vertex neighbourly 3-manifold.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Discrete Mathematics - Volume 308, Issue 22, 28 November 2008, Pages 5087–5095
نویسندگان
, ,