Introduction to Riemann surfaces
著者
書誌事項
Introduction to Riemann surfaces
AMS Chelsea Pub., 2001, c1981
2nd ed
大学図書館所蔵 全5件
  青森
  岩手
  宮城
  秋田
  山形
  福島
  茨城
  栃木
  群馬
  埼玉
  千葉
  東京
  神奈川
  新潟
  富山
  石川
  福井
  山梨
  長野
  岐阜
  静岡
  愛知
  三重
  滋賀
  京都
  大阪
  兵庫
  奈良
  和歌山
  鳥取
  島根
  岡山
  広島
  山口
  徳島
  香川
  愛媛
  高知
  福岡
  佐賀
  長崎
  熊本
  大分
  宮崎
  鹿児島
  沖縄
  韓国
  中国
  タイ
  イギリス
  ドイツ
  スイス
  フランス
  ベルギー
  オランダ
  スウェーデン
  ノルウェー
  アメリカ
注記
Reprint. Originally published: New York : Chelsea Pub. Co., c1981; 2nd ed
Bibliography: p. 301-303
Includes index
内容説明・目次
内容説明
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.
目次
- Introduction:
- 1-1 Algebraic functions and Riemann surfaces
- 1-2 Plane fluid flows
- 1-3 Fluid flows on surfaces
- 1-4 Regular potentials
- 1-5 Meromorphic functions
- 1-6 Function theory on a torus General Topology:
- 2-1 Topological spaces
- 2-2 Functions and mappings
- 2-3 Manifolds Riemann Surface of an Analytic Function:
- 3-1 The complete analytic function
- 3-2 The analytic configuration Covering Manifolds:
- 4-1 Covering manifolds
- 4-2 Monodromy theorem
- 4-3 Fundamental group
- 4-4 Covering transformations Combinatorial Topology:
- 5-1 Triangulation
- 5-2 Barycentric coordinates and subdivision
- 5-3 Orientability
- 5-4 Differentiable and analytic curves
- 5-5 Normal forms of compact orientable surfaces
- 5-6 Homology groups and Betti numbers
- 5-7 Invariance of the homology groups
- 5-8 Fundamental group and first homology group
- 5-9 Homology on compact surfaces Differentials and Integrals:
- 6-1 Second-order differentials and surface integrals
- 6-2 First-order differentials and line integrals
- 6-3 Stokes' theorem
- 6-4 The exterior differential calculus
- 6-5 Harmonic and analytic differentials The Hilbert Space of Differentials:
- 7-1 Definition and properties of Hilbert space
- 7-2 Smoothing operators
- 7-3 Weyl's lemma and orthogonal projections Existence of Harmonic and Analytic Differentials:
- 8-1 Existence theorems
- 8-2 Countability of a Riemann surface Uniformization:
- 9-1 Schlichtartig surfaces
- 9-2 Universal covering surfaces
- 9-3 Triangulation of a Riemann surface
- 9-4 Mappings of a Riemann surface onto itself Compact Riemann Surfaces:
- 10-1 Regular harmonic differentials
- 10-2 The bilinear relations of Riemann
- 10-3 Bilinear relations for differentials with singularities
- 10-4 Divisors
- 10-5 The Riemann-Roch theorem
- 10-6 Weierstrass points
- 10-7 Abel's theorem
- 10-8 Jacobi inversion problem
- 10-9 The field of algebraic functions
- 10-10 The hyperelliptic case References Index.
「Nielsen BookData」 より