Riemann surfaces

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This is an authoritative but accessible text on one dimensional complex manifolds or Riemann surfaces. Dealing with the main results on Riemann surfaces from a variety of points of view the book pulls together materials from global analysis topology, and algebraic geometry, and covers the essential mathematical methods and tools.

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Title Statements

Full title :Riemann surfaces / Simon Donaldson.

Summary

Edition Statements

Publication Date:2011.

Publication Statements

Publisher(s):Oxford University Press
Place of Publication:Oxford
Language:eng
Publication Date:2011.

The Physical Object

Description:1 online resource (xiii, 286 pages) : : illustrations

Edition Identifiers

ISBN:9780191545849, 0191545848, 1299990290, 9781299990296
oclc:ocn861200296
LC Classification:QA333
Dewey Decimal:515.9/3

Cover; Contents; PART I: PRELIMINARIES; 1 Holomorphic functions; 1.1 Simple examples: algebraic functions; 1.2 Analytic continuation: differential equations; Exercises; 2 Surface topology; 2.1 Classification of surfaces; 2.2 Discussion: the mapping class group; Exercises; PART II: BASIC THEORY; 3 Basic definitions; 3.1 Riemann surfaces and holomorphic maps; 3.2 Examples; Exercises; 4 Maps between Riemann surfaces; 4.1 General properties; 4.2 Monodromy and the Riemann Existence Theorem; Exercises; 5 Calculus on surfaces; 5.1 Smooth surfaces; 5.2 de Rham cohomology.

5.3 Calculus on Riemann surfacesExercises; 6 Elliptic functions and integrals; 6.1 Elliptic integrals; 6.2 The Weierstrass [Omitted] function; 6.3 Further topics; Exercises; 7 Applications of the Euler characteristic; 7.1 The Euler characteristic and meromorphic forms; 7.2 Applications; Exercises; PART III: DEEPER THEORY; 8 Meromorphic functions and the Main Theorem for compact Riemann surfaces; 8.1 Consequences of the Main Theorem; 8.2 The Riemann-Roch formula; Exercises; 9 Proof of the Main Theorem; 9.1 Discussion and motivation; 9.2 The Riesz Representation Theorem.

9.3 The heart of the proof9.4 Weyl's Lemma; Exerci…