Modules / Lectures
Module NameDownloadDescriptionDownload Size
Definitions and Examples of Riemann SurfacesLecture 1The Idea of a Riemann Surface78 kb
Definitions and Examples of Riemann SurfacesLecture 2Simple Examples of Riemann Surfaces65 kb
Definitions and Examples of Riemann SurfacesLecture 3Maximal Atlases and Holomorphic Maps of Riemann Surfaces69 kb
Definitions and Examples of Riemann SurfacesLecture 4A Riemann Surface Structure on a Cylinder90 kb
Definitions and Examples of Riemann SurfacesLecture 5A Riemann Surface Structure on a Torus60 kb
Classification of Riemann SurfacesLecture 6Riemann Surface Structures on Cylinders and Tori via Covering Spaces68 kb
Classification of Riemann SurfacesLecture 7Moebius Transformations Make up Fundamental Groups of Riemann Surfaces55 kb
Classification of Riemann SurfacesLecture 8Homotopy and the First Fundamental Group67 kb
Classification of Riemann SurfacesLecture 9A First Classification of Riemann Surfaces50 kb
Module NameDownloadDescriptionDownload Size
Definitions and Examples of Riemann SurfacesAssignment 1The Idea of a Riemann Surface121 kb
Definitions and Examples of Riemann SurfacesAssignment 2Simple Examples of Riemann Surfaces141 kb
Definitions and Examples of Riemann SurfacesAssignment 3Maximal Atlases and Holomorphic Maps of Riemann Surfaces251 kb
Definitions and Examples of Riemann SurfacesAssignment 4A Riemann Surface Structure on a Cylinder349 kb
Definitions and Examples of Riemann SurfacesAssignment 5A Riemann Surface Structure on a Torus217 kb
Classification of Riemann SurfacesAssignment 6Riemann Surface Structures on Cylinders and Tori via Covering Spaces131 kb
Classification of Riemann SurfacesAssignment 7Moebius Transformations Make up Fundamental Groups of Riemann Surfaces116 kb
Classification of Riemann SurfacesAssignment 8Homotopy and the First Fundamental Group245 kb
Classification of Riemann SurfacesAssignment 9A First Classification of Riemann Surfaces74 kb

Sl.No Chapter Name English
1The Idea of a Riemann SurfacePDF unavailable
2Simple Examples of Riemann SurfacesPDF unavailable
3Maximal Atlases and Holomorphic Maps of Riemann SurfacesPDF unavailable
4A Riemann Surface Structure on a CylinderPDF unavailable
5A Riemann Surface Structure on a TorusPDF unavailable
6Riemann Surface Structures on Cylinders and Tori via Covering SpacesPDF unavailable
7Moebius Transformations Make up Fundamental Groups of Riemann SurfacesPDF unavailable
8Homotopy and the First Fundamental GroupPDF unavailable
9A First Classification of Riemann SurfacesPDF unavailable
10The Importance of the Path-lifting PropertyPDF unavailable
11Fundamental groups as Fibres of the Universal covering Space PDF unavailable
12The Monodromy ActionPDF unavailable
13The Universal covering as a Hausdorff Topological Space PDF unavailable
14The Construction of the Universal Covering Map PDF unavailable
15 Completion of the Construction of the Universal Covering: Universality of the Universal CoveringPDF unavailable
16 Completion of the Construction of the Universal Covering: The Fundamental Group of the base as the Deck Transformation GroupPDF unavailable
17The Riemann Surface Structure on the Topological Covering of a Riemann SurfacePDF unavailable
18Riemann Surfaces with Universal Covering the Plane or the SpherePDF unavailable
19Classifying Complex Cylinders: Riemann Surfaces with Universal Covering the Complex PlanePDF unavailable
20Characterizing Moebius Transformations with a Single Fixed PointPDF unavailable
21Characterizing Moebius Transformations with Two Fixed PointsPDF unavailable
22Torsion-freeness of the Fundamental Group of a Riemann SurfacePDF unavailable
23Characterizing Riemann Surface Structures on Quotients of the Upper Half-Plane with Abelian Fundamental GroupsPDF unavailable
24Classifying Annuli up to Holomorphic IsomorphismPDF unavailable
25Orbits of the Integral Unimodular Group in the Upper Half-PlanePDF unavailable
26Galois Coverings are precisely Quotients by Properly Discontinuous Free ActionsPDF unavailable
27Local Actions at the Region of Discontinuity of a Kleinian Subgroup of Moebius TransformationsPDF unavailable
28Quotients by Kleinian Subgroups give rise to Riemann SurfacesPDF unavailable
29The Unimodular Group is KleinianPDF unavailable
30The Necessity of Elliptic Functions for the Classification of Complex ToriPDF unavailable
31The Uniqueness Property of the Weierstrass Phe-function associated to a Lattice in the PlanePDF unavailable
32The First Order Degree Two Cubic Ordinary Differential Equation satisfied by the Weierstrass Phe-functionPDF unavailable
33The Values of the Weierstrass Phe-function at the Zeros of its Derivative are nonvanishing Analytic Functions on the Upper Half-PlanePDF unavailable
34The Construction of a Modular Form of Weight Two on the Upper Half-PlanePDF unavailable
35The Fundamental Functional Equations satisfied by the Modular Form of Weight Two on the Upper Half-PlanePDF unavailable
36The Weight Two Modular Form assumes Real Values on the Imaginary Axis in the Upper Half-planePDF unavailable
37The Weight Two Modular Form Vanishes at InfinityPDF unavailable
38The Weight Two Modular Form Decays Exponentially in a Neighbourhood of InfinityPDF unavailable
39A Suitable Restriction of the Weight Two Modular Form is a Holomorphic Conformal Isomorphism onto the Upper Half-PlanePDF unavailable
40The J-Invariant of a Complex Torus (or) of an Algebraic Elliptic CurvePDF unavailable
41A Fundamental Region in the Upper Half-Plane for the Elliptic Modular J-InvariantPDF unavailable
42The Fundamental Region in the Upper Half-Plane for the Unimodular GroupPDF unavailable
43A Region in the Upper Half-Plane Meeting Each Unimodular Orbit Exactly OncePDF unavailable
44Moduli of Elliptic CurvesPDF unavailable
45Punctured Complex Tori are Elliptic Algebraic Affine Plane Cubic Curves in Complex 2-SpacePDF unavailable
46The Natural Riemann Surface Structure on an Algebraic Affine Nonsingular Plane CurvePDF unavailable
47Complex Projective 2-Space as a Compact Complex Manifold of Dimension TwoPDF unavailable
48Complex Tori are the same as Elliptic Algebraic Projective CurvesPDF unavailable


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