This Concept Map, created with IHMC CmapTools, has information related to: Identification of preferred extremals of Kaehler action, TGD as almost topological QFT hypothesis favours space-time surfaces possessing so called Hamilton-Jacobi structure, preferred extremals as space-time surfaces which are associative or co-associative in particular associative/co- associative space-time surfaces suggested to be identifiable as 4-surfaces of M^4xCP_2 assigned to octonion real analytic maps of complexifed octonions, one of the basic challenges of TGD although the vacuum degeneracy of Kaehler action, very large classes of extremals are known such as cosmic strings, Kaehler action to 3-D Chern-Simons terms if weak form of electric-magnetic duality implying enormous calculational simplification is satisfied, IDENTIFICATION OF PREFERRED EXTREMALS OF KAEHLER ACTION remains one of the basic challenges of TGD, one of the basic challenges of TGD although very large classes of extremals are known, one of the basic challenges of TGD although TGD as almost topological QFT hypothesis, a lot of qualitative information about preferred extremals (4-D spin glass degeneracy) and motivates zero energy ontology, there are several educated guesses consistent with what is known about extremals of Kaehler action such as preferred extremals as space-time surfaces which are associative or co-associative, one of the basic challenges of TGD although there are several educated guesses consistent with what is known about extremals of Kaehler action, very large classes of extremals are known such as CP_2 type vacuum extremals, TGD as almost topological QFT hypothesis reduces Kaehler action to 3-D Chern-Simons terms, space-time surfaces possessing so called Hamilton-Jacobi structure generalizing complex structure, the vacuum degeneracy of Kaehler action provides a lot of qualitative information about preferred extremals (4-D spin glass degeneracy), space-time surfaces possessing so called Hamilton-Jacobi structure providing rather detailed physical picture about the structure of preferred extremals, very large classes of extremals are known such as massless extremals (MEs) or topological light rays, associative/co- associative space-time surfaces suggested to be identifiable as 4-surfaces of M^4xCP_2 assigned to octonion real analytic maps of complexifed octonions so that analytic functions of real variable would code for space-time surfaces, Kaehler action to 3-D Chern-Simons terms if j^αA_α term in the expression of Kaehler action vanishes, there are several educated guesses consistent with what is known about extremals of Kaehler action such as space-time surfaces possessing so called Hamilton-Jacobi structure