I understand the duality in the case of homology and de Rham cohomology. Through integration a chain can be understood as a linear functional on differential forms and vice versa.
Is there a way to understand cohomotopy classes as functionals on a homotopy group? Is there a different sense in which it is dual?
I am aware of a similarly titled question but that was more about relating cohomotopy to cohomology rather than to homotopy.