Singular Homology
Singular Homology is a mathematical concept used in the field of algebraic topology to study the shape and structure of topological spaces. It assigns a sequence of abelian groups or modules to a space, which helps to classify its features, such as holes of different dimensions. This method involves considering continuous maps from standard geometric shapes, like points and circles, into the space.
The main idea behind singular homology is to analyze how these shapes can be mapped into a given space and to understand the relationships between these mappings. By examining these relationships, mathematicians can derive important information about the topology of the space, such as its connectivity and the presence of higher-dimensional holes.