Stratifications

Stratification refers to the arrangement or classification of something into different layers, levels, or strata. This concept can be applied in various fields, such as: 1. **Sociology**: Social stratification pertains to the hierarchical arrangement of individuals or groups in society based on factors such as wealth, power, education, race, and social status. It highlights inequalities and the social structures that cause different levels of access to resources and opportunities.

The Harder–Narasimhan (HN) stratification is a concept in the field of algebraic geometry, particularly in the study of moduli spaces of vector bundles over algebraic curves or more generally over varieties. It is named after mathematicians J. Harder and M. Narasimhan, who introduced this idea in the context of vector bundles. The HN stratification provides a way to organize objects (such as vector bundles) based on their stability properties.

Stratification in mathematics often refers to a method of organizing or classifying mathematical objects based on certain properties or characteristics. This concept can arise in various areas of mathematics, including: 1. **Topology**: In algebraic topology, stratification refers to a way to decompose a topological space into simpler pieces called strata, which can be more easily studied. Each stratum is a subspace that is a manifold, and the overall space is constructed from these strata.

Stratified Morse theory is a branch of mathematical study that extends classical Morse theory, which is primarily concerned with the topology of manifolds, to the setting of stratified spaces. A stratified space is a space that is decomposed into smooth manifolds, called strata, that fit together in a specific manner, often allowing for singularities in a controlled way.