Description

Book Synopsis
This is the second of a three volume collection 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 provide perspective and insight to mathematicians at all levels who are interested in geometry and topology.

Table of Contents
  • 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

    Topology as Fluid Geometry TwoDimensional Spaces

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      A Paperback by James W. Cannon

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        Book details

        Publisher American Mathematical Society
        Published 2/28/2018 12:00:00 AM
        ISBN-13 9781470437152
        978-1470437152
        ISBN-10 1470437155

        Description

        Book Synopsis
        This is the second of a three volume collection 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 provide perspective and insight to mathematicians at all levels who are interested in geometry and topology.

        Table of Contents
        • 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

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