Classical Computational Methods in Homotopy Theory 60 views

This thesis uses classical methods in algebraic topology to calculate the 2-components of stable and unstable homotopy groups. Because these groups are notoriously difficult to compute directly, we first build out the necessary algebraic tools. This involves constructing primary cohomology operations with mod 2 coefficients—specifically the Steenrod squares and the Steenrod algebra—and using tools like the Serre spectral sequence and Serre's mod C theory to handle 2-torsion. By combining these methods with Postnikov towers, we are able to explicitly compute the 2-components of the stable homotopy groups of spheres up to the 7-stem, the low-dimensional unstable homotopy groups of the 3-sphere, and the stable homotopy groups of the real projective plane.

BA (Bachelor of Arts)

Algebraic Topology; Homotopy Theory

English

2026-05-22