Homology of "World of Classical Worlds" in Relation to Floer Homology & Quantum Homology

Abstract

One of the mathematical challenges of TGD is the construction of the homology of "world of classical worlds" (WCW). The generalization of Floer homology looks rather obvious in the zero ontology (ZEO) based view about quantum TGD. ZEO, the notion of preferred extremal (PE), and the intuitive connection between the failure of strict non-determinism and criticality are essential elements. The homology group is defined in terms of the free group formed by preferred extremals PE(X₃,Y₃) for which X₃ is a stable maximum of Kahler function K associated with the passive boundary of CD and Y₃ associated with the passive boundary is a more general critical point.