1. Introduction

    1. General Coordinate Invariance and generalized quantum gravitational holography

    2. Light like 3-D causal determinants and effective 2-dimensionality

    3. Magic properties of light cone boundary and isometries of WCW

    4. Symplectic transformations of δ M4_+× CP_2 as isometries of WCW

    5. Does the symmetric space property reduce to coset construction for Super Virasoro algebras?

    6. What effective 2-dimensionality and holography really mean?

    7. Attempts to identify WCW Hamiltonians

    8. For the reader

  2. How to generalize the construction of WCW geometry to take into account the classical non-determinism?

    1. Quantum holography in the sense of quantum gravity theories

    2. How the classical determinism fails in TGD?

    3. The notions of imbedding space, 3-surface, and configuration space

    4. The treatment of non-determinism of Kähler action in zero energy ontology

    5. Category theory and WCW geometry

  3. Identification of the symmetries and coset space structure of WCW

    1. Reduction to the light cone boundary

    2. WCW as a union of symmetric spaces

  4. Complexification

    1. Why complexification is needed?

    2. The metric, conformal and symplectic structures of the light cone boundary

    3. Complexification and the special properties of the light cone boundary

    4. How to fix the complex and symplectic structures in a Lorentz invariant manner?

    5. The general structure of the isometry algebra

    6. Representation of Lorentz group and conformal symmetries at light cone boundary

    7. How the complex eigenvalues of the radial scaling operator relate to symplectic conformal weights?

  5. Magnetic and electric representations of the configuration space Hamiltonians

    1. Radial symplectic invariants

    2. Kähler magnetic invariants

    3. Isometry invariants and spin glass analogy

    4. Magnetic flux representation of the symplectic algebra

    5. Symplectic transformations of δ M4+/-

    6. Quantum counterparts of the symplectic Hamiltonians

  6. General expressions for the symplectic and Kähler forms

    1. Closedness requirement

    2. Matrix elements of the symplectic form as Poisson brackets

    3. General expressions for Kähler form, Kähler metric and Kähler function

    4. Diff(X3) invariance and degeneracy and conformal invariances of the symplectic form

    5. Complexification and explicit form of the metric and Kähler form

    6. Comparison of CP2 Kähler geometry with configuration space geometry

    7. Comparison with loop groups

    8. Symmetric space property implies Ricci flatness and isometric action of symplectic transformations

  7. Ricci flatness and divergence cancelation

    1. Inner product from divergence cancelation

    2. Why Ricci flatness

    3. Ricci flatness and Hyper Kähler property

    4. The conditions guaranteeing Ricci flatness

    5. Is WCW metric Hyper Kähler?