The proposed model, argued to overcome this problem, involves several topological elements.
- The topological explanation of the family replication phenomenon in terms of the genus of partonic 2-surface carrying fermion lines as boundaries of string world sheets.
- The view of holography as a 4-D analog of holomorphy reducing to 2-D holomorphy for partonic 2-surfaces. This predicts two kinds of partonic 2-surfaces as complex 2-surfaces in CP2 with a spherical topology. Tor the homologically non-trivial geodesic sphere induced weak fields vanish (no parity violation classically) and for the second complex sphere they do not. A natural working hypothesis is that these two spheres explain the difference between strong and weak interactions.
- The homology (Kähler magnetic) charge h of the partonic 2-surface correlates with the genus of the partonic 2-surface. For complex partonic 2-surfaces in CP2, the genus is given g=(h-1)(h-2)/2-s, where s is the number of singularities. Only the genera g=(h-1)(h-2)/2 are free of singularities. For g=0, this includes h=1 and h=2. Already for g=2 there would be singularity. It is however possible to overcome this problem since partonic 2-surfaces can be deformed to M4 degrees of freedom and one can add handles in this way. A rather detailed picture of partonic 2-surfaces and monopole flux tubes emerges.
For a summary of earlier postings see Latest progress in TGD.
For the lists of articles (most of them published in journals founded by Huping Hu) and books about TGD see this.