Characteristic Class of Isotopy for Surfaces-大连理工大学数学科学学院(新)

Characteristic Class of Isotopy for Surfaces

2018年05月09日 15:01  点击:[]


报告题目:Characteristic Class of Isotopy for Surfaces



报告人:雷娜 教授(大连理工大学软件学院

报告校内联系人:雷逢春 教授 联系电话:84706472

报告摘要It is an important problem in topology to verify whether two embeddings are isotopic. This work proposes an algorithm for computing Haefliger-Wu invariant for isotopy based on algebraic topological methods.

Given a simplicial complex embedded in the Euclidean space, the deleted product of it is the direct product with diagonal removed. The Gaussian mapping transforms the deleted product to the unit sphere. The pull-back of the generator of the cohomology group of the sphere defines characteristic class of the isotopy of the embedding. By using Mayer Vietoris sequence and Künneth theorem, the computational algrothim can be greatly simplified.

We prove the ranks of homology groups of the deleted product of a closed surface and give explicit construction of the generators of the homology groups of the deleted product. Numerical experimental results show the efficiency and efficacy of the proposed method.

报告人简介:雷娜博士,于吉林大学数学学院获得理学博士学位,现为大连理工大学软件学院教授,博士生导师,兼任中国工业与应用数学学会几何设计与计算专业委员会委员;中国数学会计算机数学专业委员会委员;美国数学会 Mathematical Review评论员;清华大学数学科学中心访问教授;曾为纽约州立大学石溪分校计算机系访问教授;德克萨斯大学奥斯汀分校计算工程与科学研究所research fellow;中科院数学与系统科学研究院访问学者。The Visual Computer, Journal of Computational and Applied Mathematics, Journal of Systems Science and Complexity, SCIENCE CHINA Mathematics等国际期刊审稿人。研究方向为:应用现代微分几何和代数几何的理论与方法解决工程及医学领域的问题,主要聚焦于计算共形几何、计算拓扑、符号计算及其在计算机图形学、计算机视觉、几何建模和医学图像中的应用。


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