Hyperbolic Geometry, the Modular Group and Diophantine Approximation - Lecture 1

Hyperbolic Geometry, the Modular Group and Diophantine Approximation - Lecture 1

International Centre for Theoretical Sciences via YouTube Direct link

Let S'H be the unit tangent bundle over H

7 of 20

7 of 20

Let S'H be the unit tangent bundle over H

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Hyperbolic Geometry, the Modular Group and Diophantine Approximation - Lecture 1

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  1. 1 Start
  2. 2 Hyperbolic geometry, the modular group and Diophantine approximation Lecture - 01
  3. 3 H Hyperbolic plane
  4. 4 Boundary of H
  5. 5 Subgroups of SL2,R
  6. 6 Observation
  7. 7 Let S'H be the unit tangent bundle over H
  8. 8 Observation:
  9. 9 Hence
  10. 10 Geodesic flow
  11. 11 Observation
  12. 12 Note
  13. 13 Recall
  14. 14 Example
  15. 15 Fundamental domains
  16. 16 Dirichlet fundamental domain
  17. 17 Proposition
  18. 18 Proof
  19. 19 Claim
  20. 20 Imaginary part

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