Скачать или смотреть Algebraic Topology in Python: Simplicial Complexes and Persistent Homology

Algebraic topology is a branch of mathematics that uses tools from abstract algebra to study the topological properties of spaces. One of the key concepts in algebraic topology is the idea of a simplicial complex, which is a way of discretizing a space into simple building blocks. In this video, we explore how to work with simplicial complexes in Python using the Gudhi library.

We will cover the basics of simplicial complexes, including how to create and manipulate them, as well as how to compute their topological properties using persistent homology. Persistent homology is a method for analyzing the topological features of a space at different scales, and it has many applications in data analysis and machine learning.


For those who want to delve deeper into algebraic topology, I recommend starting with the basics of point-set topology and group theory. A good resource for this is the textbook "Algebraic Topology" by Allen Hatcher. Additionally, the Gudhi library has extensive documentation and tutorials that can help you get started with working with simplicial complexes in Python.


Some suggestions to reinforce your study of algebraic topology include:

Experimenting with different simplicial complexes and computing their persistent homology
Reading about the applications of algebraic topology in data analysis and machine learning
Exploring other libraries and tools for working with algebraic topology, such as Scipy and Mayavi


Additional Resources:
Gudhi library documentation: https://gudhi.inria.fr/doc/latest/
"Algebraic Topology" by Allen Hatcher: https://www.math.cornell.edu/~hatcher...

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