图 书 馆
推广整数,同调计算AT模型的概念Extending the Notion of AT-Models for Integer Homology Computation |
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| 课程网址: | http://videolectures.net/gbr07_real_etn/ |
| 主讲教师: | Pedro Real |
| 开课单位: | 塞维利亚大学 |
| 开课时间: | 2007-07-12 |
| 课程语种: | 英语 |
| 中文简介: |  |
| 课程简介: | When the ground ring is a field, the notion of algebraic topological model (AT-model) is a useful tool for computing (co)homology, representative (co)cycles of (co)homology generators and the cup product on cohomology of nD digital images as well as for controlling topological information when the image suffers local changes. In this paper, we formalize the notion of lambda-AT-model (lambda being an integer) which extends the one of AT-model and allows the computation of homological information in the integer domain without computing the Smith Normal Form of the boundary matrices. We present an algorithm for computing such a model, obtaining Betti numbers, the prime numbers p involved in the invariant factors (corresponding to the torsion subgroup of the homology), the amount of invariant factors that are a power of p and a set of representative cycles of the generators of homology mod p, for such p. |
| 关 键 词: | 代数拓扑模型; 同源性; 素数 |
| 课程来源: | 视频讲座网 |
| 最后编审: | 2019-04-15：cwx |
| 阅读次数: | 99 |