1. Introduction

    1. What Are The Deep Problems?

    2. TGD Background

    3. Homology And Cohomology Theories Based On Groups Algebras For A Hierarchy Of Galois Groups Assigned To Polynomials Defined By Infinite Primes

    4. P-Adic Integration And Cohomology

    5. Topics Related To TGD-String Theory Correspondence

    6. P-Adic Space-Time Sheets As Correlates For Boolean Cognition

  2. Some Backgbround About Homology And Cohomology

    1. Basic Ideas Of Algebraic Geometry

    2. Algebraization Of Intersections And Unions Of Varieties

    3. Motivations For Motives

  3. Examples Of Cohomologies

    1. Etale Cohomology And L-Adic Cohomology

    2. Crystalline Cohomology

    3. Motivic Cohomology

  4. Infinite Rationals Define Rational Functions Of Several Variables: A Possible Number Theoretic Generalization For The Notions Of Homotopy, Homology, And Cohomology

    1. Infinite Rationals And Rational Functions Of Several Variables

    2. Galois Groups As Non-Commutative Analogs Of Homotopy Groups

    3. Generalization Of The Boundary Operation

    4. Could Galois Groups Lead To Number TheoreticalGeneralizations Of Homology And Cohomology Groups?

    5. What Is The Physical Interpretation Of The Braided Galois Homology

    6. Is There A Connection With The Motivic Galois Group?

  5. Motives And Twistor Approach Applied To TGD

    1. Number Theoretic Universality, Residue Integrals, AndSymplectic Symmetry

    2. How To Define The P-Adic Variant For The Exponent Of K\"ahler Action?

    3. Motivic Integration

    4. How Could One Calculate P-Adic Integrals Numerically?

    5. Infinite Rationals And Multiple Residue Integrals As Galois Invariants

    6. Twistors, Hyperbolic 3-Manifolds, And Zero Energy Ontology

  6. Floer Homology And TGD

    1. Trying To Understand The Basic Ideas Of Floer Homology

    2. Could Floer Homology Teach Something New About Quantum TGD?

  7. Could Gromov-Witten Invariants And Braided Galois Homology Together Allow To Construct WCW Spinor Fields?

    1. Gromov-Witten Invariants

    2. Gromov-Witten Invariants And Topological String Theory Of Type A

    3. Gromov-Witten Invariants And WCW Spinor Fields In Zero Mode Degrees Of Freedom

  8. K-Theory, Branes, And TGD

    1. Brane World Scenario

    2. The Basic Challenge: Classify The Conserved Brane Charges Associated With Branes

    3. Problems

    4. What Could Go Wrong With Super String Theory And How TGD Circumvents The Problems?

    5. Can One Identify The Counterparts Of R-R And NS-NS Fields In TGD?

    6. What About Counterparts Of $S$ And $U$ Dualities In TGD Framework?

    7. Could One Divide Bundles?

  9. A Connection Between Cognition, Number Theory, Algebraic Geometry, Topology, And Quantum Physics

    1. Innocent Questions

    2. Stone Theorem And Stone Spaces

    3. 2-Adic Integers And 2-Adic Numbers As Stone Spaces

    4. What About P-Adic Integers With $P>2$?

    5. One More Road To TGD

    6. A Connection Between Cognition And Algebraic Geometry

    7. Quantum Mathematics

  10. Boolean algebras, Stone spaces and p-adic physics

    1. Boolean algebras

    2. Stone spaces

    3. Stone spaces and TGD