This well-known book is a self-contained treatment of the classical theory of abstract Riemann surfaces. The first five chapters cover the requisite function theory and topology for Riemann surfaces. The second five chapters cover differentials and uniformization. For compact Riemann surfaces, there are clear treatments of divisors, Weierstrass points, the Riemann-Roch theorem and other important topics. Springer's book is an excellent text for an introductory course on Riemann surfaces. It includes exercises after each chapter and is illustrated with a beautiful set of figures.
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1-1 Algebraic functions and Riemann surfaces. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
parametric disk, unlimited covering manifold, harmonic and analytic differentials, everywhere regular potential, real harmonic differential, lemma and orthogonal projections, normal barycentric, analytic configuration, complete analytic function, group and first homology group, piecewise analytic curve, mod periods, regular analytic function, harmonic differentials, abelian differential, universal covering surfaces, local uniformizing parameter, complex potential function, compact carrier, homotopic deformation, exterior differential calculus, euclidean disk, covering manifolds, integral divisor, nonzero period Key Phrases - Capitalized Phrases (CAPs): (learn more)
Monodromy Theorem, Combinatorial Topology New!
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1-1 Algebraic functions and Riemann surfaces. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
parametric disk, unlimited covering manifold, harmonic and analytic differentials, everywhere regular potential, real harmonic differential, lemma and orthogonal projections, normal barycentric, analytic configuration, complete analytic function, group and first homology group, piecewise analytic curve, mod periods, regular analytic function, harmonic differentials, abelian differential, universal covering surfaces, local uniformizing parameter, complex potential function, compact carrier, homotopic deformation, exterior differential calculus, euclidean disk, covering manifolds, integral divisor, nonzero period Key Phrases - Capitalized Phrases (CAPs): (learn more)
Monodromy Theorem, Combinatorial Topology New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 15
books:
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55
books
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- Algebraic Topology (Colloquium Pbns. Series, Vol 27) by Solomon Lefschetz in Back Matter
- Automorphic Functions (AMS Chelsea Publishing) by Lester R. Ford in Back Matter
- Introduction to Topology (Mathematics Series) by Solomon Lefschetz in Back Matter
- Conformal Representation (Dover Books on Mathematics) by C. Caratheodory in Back Matter
- Riemann Surfaces (Mathematics Series) by Lars V. Ahlfors in Back Matter
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- Theory of Functions of a Complex Variable (3 Vols. in 1) by A. I. Markushevich in Back Matter (1), and Back Matter (2)
- Topics on Riemann Surfaces and Fuchsian Groups (London Mathematical Society Lecture Note Series) by E. Bujalance on page 28, and page 90
- Mathematical Theory of Diffraction (Progress in Mathematical Physics) by Arnold Sommerfeld in Back Matter (1), and Back Matter (2)
- Riemann, Topology, and Physics by Michael I. Monastyrsky on page 83, and Back Matter
- A Scrapbook of Complex Curve Theory (Graduate Studies in Mathematics, V. 55) by C. Herbert Clemens on page 101, and Back Matter
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