Modules / Lectures

Module Name | Download | Description | Download Size |
---|---|---|---|

Definitions and Examples of Riemann Surfaces | Lecture 1 | The Idea of a Riemann Surface | 78 kb |

Definitions and Examples of Riemann Surfaces | Lecture 2 | Simple Examples of Riemann Surfaces | 65 kb |

Definitions and Examples of Riemann Surfaces | Lecture 3 | Maximal Atlases and Holomorphic Maps of Riemann Surfaces | 69 kb |

Definitions and Examples of Riemann Surfaces | Lecture 4 | A Riemann Surface Structure on a Cylinder | 90 kb |

Definitions and Examples of Riemann Surfaces | Lecture 5 | A Riemann Surface Structure on a Torus | 60 kb |

Classification of Riemann Surfaces | Lecture 6 | Riemann Surface Structures on Cylinders and Tori via Covering Spaces | 68 kb |

Classification of Riemann Surfaces | Lecture 7 | Moebius Transformations Make up Fundamental Groups of Riemann Surfaces | 55 kb |

Classification of Riemann Surfaces | Lecture 8 | Homotopy and the First Fundamental Group | 67 kb |

Classification of Riemann Surfaces | Lecture 9 | A First Classification of Riemann Surfaces | 50 kb |

Sl.No | Chapter Name | English |
---|---|---|

1 | The Idea of a Riemann Surface | PDF unavailable |

2 | Simple Examples of Riemann Surfaces | PDF unavailable |

3 | Maximal Atlases and Holomorphic Maps of Riemann Surfaces | PDF unavailable |

4 | A Riemann Surface Structure on a Cylinder | PDF unavailable |

5 | A Riemann Surface Structure on a Torus | PDF unavailable |

6 | Riemann Surface Structures on Cylinders and Tori via Covering Spaces | PDF unavailable |

7 | Moebius Transformations Make up Fundamental Groups of Riemann Surfaces | PDF unavailable |

8 | Homotopy and the First Fundamental Group | PDF unavailable |

9 | A First Classification of Riemann Surfaces | PDF unavailable |

10 | The Importance of the Path-lifting Property | PDF unavailable |

11 | Fundamental groups as Fibres of the Universal covering Space | PDF unavailable |

12 | The Monodromy Action | PDF unavailable |

13 | The Universal covering as a Hausdorff Topological Space | PDF unavailable |

14 | The Construction of the Universal Covering Map | PDF unavailable |

15 | Completion of the Construction of the Universal Covering: Universality of the Universal Covering | PDF unavailable |

16 | Completion of the Construction of the Universal Covering: The Fundamental Group of the base as the Deck Transformation Group | PDF unavailable |

17 | The Riemann Surface Structure on the Topological Covering of a Riemann Surface | PDF unavailable |

18 | Riemann Surfaces with Universal Covering the Plane or the Sphere | PDF unavailable |

19 | Classifying Complex Cylinders: Riemann Surfaces with Universal Covering the Complex Plane | PDF unavailable |

20 | Characterizing Moebius Transformations with a Single Fixed Point | PDF unavailable |

21 | Characterizing Moebius Transformations with Two Fixed Points | PDF unavailable |

22 | Torsion-freeness of the Fundamental Group of a Riemann Surface | PDF unavailable |

23 | Characterizing Riemann Surface Structures on Quotients of the Upper Half-Plane with Abelian Fundamental Groups | PDF unavailable |

24 | Classifying Annuli up to Holomorphic Isomorphism | PDF unavailable |

25 | Orbits of the Integral Unimodular Group in the Upper Half-Plane | PDF unavailable |

26 | Galois Coverings are precisely Quotients by Properly Discontinuous Free Actions | PDF unavailable |

27 | Local Actions at the Region of Discontinuity of a Kleinian Subgroup of Moebius Transformations | PDF unavailable |

28 | Quotients by Kleinian Subgroups give rise to Riemann Surfaces | PDF unavailable |

29 | The Unimodular Group is Kleinian | PDF unavailable |

30 | The Necessity of Elliptic Functions for the Classification of Complex Tori | PDF unavailable |

31 | The Uniqueness Property of the Weierstrass Phe-function associated to a Lattice in the Plane | PDF unavailable |

32 | The First Order Degree Two Cubic Ordinary Differential Equation satisfied by the Weierstrass Phe-function | PDF unavailable |

33 | The Values of the Weierstrass Phe-function at the Zeros of its Derivative are nonvanishing Analytic Functions on the Upper Half-Plane | PDF unavailable |

34 | The Construction of a Modular Form of Weight Two on the Upper Half-Plane | PDF unavailable |

35 | The Fundamental Functional Equations satisfied by the Modular Form of Weight Two on the Upper Half-Plane | PDF unavailable |

36 | The Weight Two Modular Form assumes Real Values on the Imaginary Axis in the Upper Half-plane | PDF unavailable |

37 | The Weight Two Modular Form Vanishes at Infinity | PDF unavailable |

38 | The Weight Two Modular Form Decays Exponentially in a Neighbourhood of Infinity | PDF unavailable |

39 | A Suitable Restriction of the Weight Two Modular Form is a Holomorphic Conformal Isomorphism onto the Upper Half-Plane | PDF unavailable |

40 | The J-Invariant of a Complex Torus (or) of an Algebraic Elliptic Curve | PDF unavailable |

41 | A Fundamental Region in the Upper Half-Plane for the Elliptic Modular J-Invariant | PDF unavailable |

42 | The Fundamental Region in the Upper Half-Plane for the Unimodular Group | PDF unavailable |

43 | A Region in the Upper Half-Plane Meeting Each Unimodular Orbit Exactly Once | PDF unavailable |

44 | Moduli of Elliptic Curves | PDF unavailable |

45 | Punctured Complex Tori are Elliptic Algebraic Affine Plane Cubic Curves in Complex 2-Space | PDF unavailable |

46 | The Natural Riemann Surface Structure on an Algebraic Affine Nonsingular Plane Curve | PDF unavailable |

47 | Complex Projective 2-Space as a Compact Complex Manifold of Dimension Two | PDF unavailable |

48 | Complex Tori are the same as Elliptic Algebraic Projective Curves | PDF unavailable |

Sl.No | Language | Book link |
---|---|---|

1 | English | Not Available |

2 | Bengali | Not Available |

3 | Gujarati | Not Available |

4 | Hindi | Not Available |

5 | Kannada | Not Available |

6 | Malayalam | Not Available |

7 | Marathi | Not Available |

8 | Tamil | Not Available |

9 | Telugu | Not Available |