Algebraic Topology Learning Guide

This guide systematically outlines the core content of algebraic topology, progressing from foundational concepts to advanced theories, progressively constructing a knowledge framework that includes continuity, homotopy, homology, fiber bundles, and high-dimensional manifolds.

Basic Concepts and Continuity

Definitions and properties of continuity and homeomorphism

Homotopy Theory and Classification of Maps

Homological Theory and Cohomology

Construction Methods in Homological Theory

Computation of Cohomology and Its Applications

Fiber Bundle and Characteristic Class

Definition and Structure of Fiber Bundles

Topological Invariance of Characteristic Classes

High-Dimensional Manifolds and Fractals

Topological Structure of High-Dimensional Manifolds

Fractal Algebraic Topology Research