This three-volume collection is devoted to the geometry, topology, and curvature of 2-dimensional spaces. The collection provides a guided tour through a wide range of topics by one of the twentieth century's masters of geometric topology. The books are accessible to college and graduate students and provide perspective and insight to mathematicians at all levels who are interested in geometry and topology.
Rezensionen / Stimmen
The books contain an incredible range of ideas, both in terms of topic and in terms of sophistication. The author has great taste in topics and provides very valuable insights."" - Richard Evan Schwartz, Brown University
Reihe
Sprache
Verlagsort
Zielgruppe
Maße
Höhe: 254 mm
Breite: 178 mm
Gewicht
ISBN-13
978-1-4704-4323-8 (9781470443238)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Klassifikation
James W. Cannon, Brigham Young University, Provo, UT.
Volume 1
Lengths-The Pythagorean theorem
Consequences of the Pythagorean theorem
Areas
Areas by slicing and scaling
Areas by cut and paste
Areas by counting
Unsolvable problems in Euclidean geometry
Does every set have a size?
Bibliography
Volume 2
The fundamental theorem of algebra
The Brouwer fixed point theorem
Tools
Lebesgue covering dimension
Fat curves and Peano curves
The arc, the simple closed curve, and the Cantor set
Algebraic topology
Characterization of the 2-sphere
2-manifolds
Arcs in $\mathbb{S}^2$ are tame
R. L. Moore's decomposition theorem
The open mapping theorem
Triangulation of 2-manifolds
Structure and classification of 2-manifolds
The torus
Orientation and Euler characteristic
The Riemann-Hurwitz theorem
Bibliography
Volume 3
A graphical introduction to hyperbolic geometry
Hyperbolic geometry
Gravity as curvature
Curvature by polyhedral approximation
Curvature as a length derivative
Theorema egregium
Curvature appendix
Bibliography
