多个少顶点三角化2-流形的多面体嵌入与浸入
Polyhedral Embeddings and Immersions of Many Triangulated 2-Manifolds with Few Vertices
摘要：
本文对Hougardy、Lutz和Zelke在2010年首次提出的启发式算法进行了改进和扩展，用于通过单形线性嵌入实现具有较少顶点的三角化可定向曲面。改进在于对非可定向曲面（单纯形线性浸入）以及对称实现的适用性。在我们的算法的帮助下，许多-往往是对称的-实现的非可定向曲面的最小数目或很少的顶点已被首次获得。这些例子包括具有一个或两个手柄的射影平面和具有一个或两个手柄的克莱因瓶。
英文摘要：
This article presents an improvement and extension of the heuristic first presented by Hougardy, Lutz, and Zelke in 2010 for realizing triangulated orientable surfaces with few vertices by a simplex-wise linear embedding. The improvement consists in the applicability to non-orientable surfaces (simplex-wise linear immersions) as well as symmetric realizations. With the help of our algorithm, numerous - often symmetric - realizations of non-orientable surfaces with the minimal number or few vertices have been obtained for the first time. These examples include the the Projective Plane with one or two handles and the Klein Bottle with one or two handles.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
