A note on the Eilenberg-Mac Lane isomorphism for quadratic forms

Puntos clave

• The aim is to provide a straightforward proof of the Eilenberg-Mac Lane trace isomorphism connecting cohomology and quadratic forms.
• Presented an elementary proof of the Eilenberg-Mac Lane trace isomorphism.
• Developed explicit constructions related to quadratic forms and bilinear forms.
• Characterized conditions for expressing quadratic forms as traces of bilinear forms for various coefficient groups.
• Established a clear isomorphism between the third 2-abelian cohomology group and quadratic forms.
• Identified specific conditions under which quadratic forms can be expressed as traces of bilinear forms.