基于计算同调的映射度数值计算

12th GAMM - IMACS International Symposium on Scientific Computing, Computer Arithmetic and Validated Numerics (SCAN 2006) Pub Date : 2006-09-26 DOI:10.1109/SCAN.2006.32

K. Nakakura, S. Murashige

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引用次数: 1

摘要

本文描述了d维球Bd上连续映射f: Bd) Rd的映射度度(f, Bd)的数值计算，其中d为Z和ges2。映射度可以用在同态群上的同态来定义。提出了一种无需直接计算同态群即可计算同态的有效方法，并利用计算同态获得映射度。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Numerical Computation of the Mapping Degree using Computational Homology

This paper describes numerical computation of the mapping degree deg(f, Bd)for a continuous map f : Bd) Rd on the d-dimensional ball Bd where d isin Z and ges2. The mapping degree can be defined using a homomorphism which is induced on homology groups. We propose an efficient method to compute the homomorphism without direct calculation of homology groups, and obtain the mapping degree using computational homology.

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12th GAMM - IMACS International Symposium on Scientific Computing, Computer Arithmetic and Validated Numerics (SCAN 2006)

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