Tunnekohdan

Tunnekohdan, also known as tunneling cohomology, is a mathematical concept used in the study of topological spaces and their properties. It was introduced by John R. Stallings in the 1960s as a tool to understand the homotopy type of a space. Tunnekohdan is particularly useful in the context of homotopy theory, a branch of algebraic topology that studies the continuous mappings between topological spaces.

The fundamental idea behind tunnekohdan is to associate a cohomology theory to a space that captures its homotopy type. This is done by constructing a spectral sequence, known as the tunnekohdan spectral sequence, which converges to the cohomology of the space. The tunnekohdan spectral sequence is built using the singular cohomology of the space and its associated Postnikov towers.

One of the key features of tunnekohdan is its ability to detect the homotopy groups of a space. The tunnekohdan spectral sequence provides a way to compute the homotopy groups of a space by analyzing the differentials in the spectral sequence. This makes tunnekohdan a powerful tool in the study of homotopy theory.

Tunnekohdan has found applications in various areas of mathematics, including algebraic geometry and the study of manifolds. It has also been used in the classification of topological spaces and the study of their homotopy types. Despite its power, tunnekohdan remains a relatively specialized tool in the mathematical toolbox, used by experts in homotopy theory and related fields.