Geometric Topology in Dimensions 2 and 3

Description

Geometric topology may roughly be described as the branch of the topology of manifolds which deals with questions of the existence of homeomorphisms. Only in fairly recent years has this sort of topology achieved a sufficiently high development to be given a name, but its beginnings are easy to identify. The first classic result was the SchOnflies theorem (1910), which asserts that every 1-sphere in the plane is the boundary of a 2-cell. In the next few decades, the most notable affirmative results were the "Schonflies theorem" for polyhedral 2-spheres in space, proved by J. W. Alexander [Ad, and the triangulation theorem for 2-manifolds, proved by T. Rad6 [Rd. But the most striking results of the 1920s were negative. In 1921 Louis Antoine [A ] published an extraordinary paper in which he 4 showed that a variety of plausible conjectures in the topology of 3-space were false. Thus, a (topological) Cantor set in 3-space need not have a simply connected complement; therefore a Cantor set can be imbedded in 3-space in at least two essentially different ways; a topological 2-sphere in 3-space need not be the boundary of a 3-cell; given two disjoint 2-spheres in 3-space, there is not necessarily any third 2-sphere which separates them from one another in 3-space; and so on and on. The well-known "horned sphere" of Alexander [A ] appeared soon thereafter.

Get the book

Amazon.com

Search the book

eBay.com

Search the book

Other editions

• 

  Geometric Topology in Dimensions 2 and 3

  • 2013-06-29
  • 272 pages
  • Ebook
  • Springer Science & Business Media
• 

  Geometric Topology in Dimensions 2 and 3

  • 2013-06-11
  • 262 pages
  • Paperback
  • Springer

Similar books

• 

  Geometric Topology in Dimensions 2 and 3

  By Edwin E. Moïse

  Geometric Topology in Dimensions 2 and 3

• 

  Geometric Topology

  By James C. Cantrell

  The book is comprised of contributions from leading experts in the field of geometric topology.These contributions are grouped into four sections: low dimensional manifolds, topology of manifolds, shape theory and infinite dimensional ...

• 

  Selected Applications of Geometry to Low-dimensional Topology

  By Feng Luo, Michael H. Freedman

  C. Rourke and B. Sanderson, Introduction to Piecewise-Linear Topology, Springer, Berlin, 1972. S. Sedlacek, A direct method for minimizing the Yang-Mills functional, Comm. Math. Phys. 86 (1982), 515–528. H. Shapiro, (unpublished).

• 

  Geometric topology: 1993 Georgia International Topology Conference, August 2-13, 1993, University of Georgia, Athens, Georgia

  By William Hilal Kazez

  This is Part 1 of a two-part volume reflecting the proceedings of the 1993 Georgia International Topology Conference held at the University of Georgia during the month of August.

• 

  Handbook of Geometric Topology

  By R.B. Sher, R.J. Daverman

  B.H. Bowditch, Treelike structures arising from continua and convergence groups, Mem. Amer. Math. Soc., to appear. M.R. Bridson and G.A. Swarup, On Hausdorff-Gromov convergence and a theorem of Paulin, Enseign. Math. 40 (1994), 267–289.

• 

  Geometric Topology: Proceedings of the Geometric Topology Conference held at Park City Utah, February 19-22, 1974

  By L.C. Glaser, T.B. Rushing

  Geometric Topology: Proceedings of the Geometric Topology Conference held at Park City Utah, February 19-22, 1974

• 

  Differential Topology, Foliations, and Group Actions

  By Steven Hurder, Workshop on Topology

  This volume contains the proceedings of the Workshop on Topology held at the Pontificia Universidade Catolica in Rio de Janeiro in January 1992.

• 

  Geometric Topology: Joint U.S.-Israel Workshop on Geometric Topology, June 10-16, 1992, Technion, Haifa, Israel

  By Cameron Gordon, Yoav Moriah, Bronislaw Wajnryb

  This volume contains the refereed proceedings of the conference.

• 

  A First Course in Geometric Topology and Differential Geometry

  By Ethan D. Bloch

  ... Amer . J. Math . 62 ( 1940 ) , 243–248 . Allendoerfer , C. B. , and Weil , A. , The Gauss - Bonnet theorem for ... T. , Critical points and curvature for embedded polyhedra , J. Diff . Geom . 1 ( 1967 ) , 245–256 . " Critical points and ...

• 

  An Introduction to Geometric Topology

  By Bruno Martelli

  This book provides a self-contained introduction to the topology and geometry of surfaces and three-manifolds.