A note on the Eilenberg-Mac Lane isomorphism for quadratic forms
Abstract
We give an elementary proof of the Eilenberg-Mac Lane trace isomorphism between the third 2-abelian cohomology group and quadratic forms. Our approach yields explicit constructions and we characterize when quadratic forms can be expressed as traces of bilinear forms for arbitrary coefficient groups.
Fields of Study & Subjects
Homotopy and Cohomology in Algebraic Topology
Advanced Topics in Algebra
Advanced Operator Algebra Research
Publication details
- Journal / source
- Proceedings of the American Mathematical Society
- Volume
- 154
- Issue
- 5
- Pages
- 1927–1941
- Publication date
- 10 February 2026
- Language
- EN