A general method of constructing multi-valued functionals (Q579669)

A general method of constructing multivalued functionals on the function space of null-homotopic maps from spheres to manifolds (or simplicial complexes), via a reformulation of the homotopy periods in Sullivan theory, was proposed by \textit{S. P. Novikov} [Usp. Mat. Nauk 39, No.5(239), 97-106 (1984; Zbl 0619.58002)]. This note gives a (slight) modification of Novikov's method, by making a choice which severely restricts the indeterminacy. According to this choice, the multivalues only differ by homotopy periods, and consequently a lattice of dual homotopy elements may be constructed with the property that the corresponding functionals are quantized (single-valued).