- Overview
- Outline of a Course I
- Outline of a Course II
- Outline of a course III
- Lecture I: K-theory and Sewing Conditions
- Motivation
- Topological Field Theories
- 2D Case
- Coherence of Sewing
- The Cylinder Axiom
- Frobenius Condition
- The Closed String Sewing Theorem
- Computing the Amplitudes I
- Computing the Amplitudes II
- Generalizing the Target
- Frobenius Algebra Examples
- Frobenius Algebra Example III
- Frobenius Algebra Example IV: LG Models
- Frobenius Algebra Example V: Cosmology
- Closed and Open TFT
- Closed and Open: Categories
- Axioms for the Open Sector I
- Axioms for the Open Sector II
- Open/Closed Transition
- Open and Closed Relations I
- Open and Closed Relations II
- The Double-Twist Diagram
- The "Cardy Condition"
- The Open and Closed Sewing Theorem
- Semisimple Frobenius Algebras
- Examples
- Emergence of the "Spacetime" from an Algebra: Gelfand's Theorem I
- Gelfand's Theorem II
- Example
- Emergence of Vector Bundles I
- Emergence of Vector Bundles II
- Emergence of Vector Bundles III
- Emergence of Vector Bundles IV
- Mixed Boundary Conditions
- Mixed Boundary Conditions: Interpretation via Categories
- Mixed Boundary Conditions: Conclusion
- K-theory
- The Boundary State
- Remarks on (Semisimple) Boundary States
- Boundary States as Hole Adding Operators
- Extension to Families: vect -> K
- Example
- Baby Model of String Field Theory
- Grothendieck Group
- Fin.Gen. Projective Modules
- K-theory from Projectors
- Serre-Swan Theorem I
- Serre-Swan Theorem II
- Serre-Swan Theorem III
- Morita Equivalence
- Morita Equivalence:Examples
- Summary
- Speculation on Open Strings vs. Closed Strings

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