Geometry and topology of manifolds : surfaces and beyond / Vicente Muñoz, Ángel González-Prieto, Juan Ángel Rojo.

• "The back-up contains a draft of the title page, copyright page, and book"-- 
• "This book represents a novel approach to differential topology. Its main focus is to give a comprehensive introduction to the classification of manifolds, with special attention paid to the case of surfaces, for which the book provides a complete classification from many points of view: topological, smooth, constant curvature, complex, and conformal. Each chapter briefly revisits basic results usually known to graduate students from an alternative perspective, focusing on surfaces. We provide full proofs of some remarkable results that sometimes are missed in basic courses (e.g., the construction of triangulations on surfaces, the classification of surfaces, the Gauss-Bonnet theorem, the degree-genus formula for complex plane curves, the existence of constant curvature metrics on conformal surfaces), and we give hints to questions about higher dimensional manifolds. Many examples and remarks are scattered through the book. Each chapter ends with an exhaustive collection of problems and a list of topics for further study."--Page 4 of printed paper wrapper. 

Ämnesord

Mångfalder (matematik)  (sao)

Algebraisk topologi  (sao)

Geometry, Differential.  (LCSH)

Algebraic topology.  (fast)

Geometry, Differential.  (fast)

Manifolds (Mathematics)  (fast)

Manifolds and cell complexes {For complex manifolds, see 32Qxx} -- Research exposition (monographs, survey articles).  (msc)

Differential geometry {For differential topology, see 57Rxx. For foundational questions of differentiable manifolds, see 58Axx} -- Research exposition (monographs, survey articles).  (msc)

Algebraic topology -- Research exposition (monographs, survey articles).  (msc)

Functions of a complex variable {For analysis on manifolds, see 58-XX} -- Riemann surfaces.  (msc)

Differential geometry {For differential topology, see 57Rxx. For foundational questions of differentiable manifolds, see 58Axx} -- Global differential geometry [See also 51H25, 58-XX; for related bund.  (msc)

Algebraic topology  (LCSH)

Manifolds (Mathematics)  (LCSH)

Klassifikation

QA613 (LCC)

514/.34 (DDC)

57-02 (msc)

Tepd (kssb/8 (machine generated))