Riemann Surfaces (Graduate Texts in Mathematics, 71)
Hershel M. Farkas, Irwin Kra
This text covers Riemann surface theory from elementary aspects to the fontiers of current research. Open and closed surfaces are treated with emphasis on the compact case, while basic tools are developed to describe the analytic, geometric, and algebraic properties of Riemann surfaces and the associated Abelian varities. Topics covered include existence of meromorphic functions, the Riemann-Roch theorem, Abel's theorem, the Jacobi inversion problem, Noether's theorem, and the Riemann vanishing theorem. A complete treatment of the uniformization of Riemann sufaces via Fuchsian groups, including branched coverings, is presented, as are alternate proofs for the most important results, showing the diversity of approaches to the subject. Of interest not only to pure mathematicians, but also to physicists interested in string theory and related topics.
Rok:
2012
Wydanie:
Softcover reprint of the original 2nd ed. 1992
Wydawnictwo:
Springer
Język:
english
Strony:
382
ISBN 10:
1461273919
ISBN 13:
9781461273912
Plik:
DJVU, 3.21 MB
IPFS:
,
english, 2012
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