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Topology as Fluid Geometry: Two-Dimensional Spaces, Volume 2
About this Title
James W. Cannon, Brigham Young University, Provo, UT
Publication: AMS Non-Series Monographs
Publication Year:
2017; Volume 109
ISBNs: 978-1-4704-3715-2 (print); 978-1-4704-4305-4 (online)
DOI: https://doi.org/10.1090/mbk/109
Table of Contents
Front/Back Matter
Chapters
- 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