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Characteristic Class of Isotopy for Surfaces



Academic Report

Title: Characteristic Class of Isotopy for Surfaces

Reporter: Prof. LEI Na (School of software, Dalian University of Technology)

Time: May 21, 2018 (Monday) PM 15:30-17:00

Location: A1101# room, Innovation Park Building

Contact: Prof. LEI Fengchun (tel:84706472)

Abstract: 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.

The brief introduction to the reporter: She received a doctorate of science from the school of mathematics at the Jilin University. She is now a professor and doctoral supervisor in the school of software of Dalian University of Technology. She also serves as a member of the Geometric design and calculation of Specialized Committee of the Society of Industry and Applied Mathematics of China, a member of the computer mathematics Specialized Committee of the Chinese Mathematics Society, the Mathematical Review commentator of the American Mathematics Society and the visiting professor at the center for Mathematical Sciences, Tsinghua University. She was also a vsiting professor of computer department at State University of New York at Stony Brook, a research fellow of the Institute of Computational Engineering and science at University of Texas at Austin and a visiting scholar at the Institute of mathematics and systems science, Chinese Academy of Sciences. She is the international journal reviewers of  The Visual Computer, Journal of Computational and Applied Mathematics, Journal of Systems Science and Complexity, SCIENCE CHINA Mathematics. Her main research field is the application of modern differential geometry and algebraic geometry to solve engineering and medical problems. It focuses on conformal geometry, computing topology, symbolic computation and their applications in computer graphics, computer vision, geometric modeling and medical images.