Morse-Based Fibering of the Rank Invariant

Morse-Based Fibering of the Rank Invariant

Applied Algebraic Topology Network via YouTube Direct link

Computing the Rank Invariant by Fibration

10 of 14

10 of 14

Computing the Rank Invariant by Fibration

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Classroom Contents

Morse-Based Fibering of the Rank Invariant

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  1. 1 Intro
  2. 2 Outline
  3. 3 Multi-Parameter Persistence
  4. 4 Multi-Parameter Filtration
  5. 5 Discrete Morse Theory: Compatibility with Filtration
  6. 6 Importance of Critical Values of K
  7. 7 The Set of Critical Values
  8. 8 Partitioning R by C
  9. 9 Computing the Rank Invariant from Critical Values
  10. 10 Computing the Rank Invariant by Fibration
  11. 11 Creating Equivalence Classes of Lines
  12. 12 Using Push to Calculate the Persistence Diagram of a Lil
  13. 13 Equivalences Classes of Lines
  14. 14 Diagrams Along Equivalent Lines are in Bijection

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