Geometric Topology in Dimensions 2 and 3
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 iden...
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| Format: | eBook |
| Language: | English |
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New York, NY
Springer New York
1977, 1977
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| Edition: | 1st ed. 1977 |
| Series: | Graduate Texts in Mathematics
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| Subjects: | |
| Online Access: | |
| Collection: | Springer Book Archives -2004 - Collection details see MPG.ReNa |
Table of Contents:
- 0 Introduction
- 1 Connectivity
- 2 Separation properties of polygons in R2
- 3 The Schönflies theorem for polygons in R2
- 4 The Jordan curve theorem
- 5 Piecewise linear homeomorphisms
- 6 PL approximations of homeomorphisms
- 7 Abstract complexes and PL complexes
- 8 The triangulation theorem for 2-manifolds
- 9 The Schönflies theorem
- 10 Tame imbedding in R2
- 11 Isotopies
- 12 Homeomorphisms between Cantor sets
- 13 Totally disconnected compact sets in R2
- 14 The fundamental group (summary)
- 15 The group of (the complement of) a link
- 16 Computations of fundamental groups
- 17 The PL Schönflies theorem in R3
- 18 The Antoine set
- 19 A wild arc with a simply connected complement
- 20 A wild 2-sphere with a simply connected complement
- 21 The Euler characteristic
- 22 The classification of compact connected 2-manifolds
- 23 Triangulated 3-manifolds
- 24 Covering spaces
- 25 The Stallings proof of the loop theorem of Papakyriakopoulos
- 26 Bicollar neighborhoods; an extension of the loop theorem
- 27 The Dehn lemma
- 28 Polygons in the boundary of a combinatorial solid torus
- 29 Limits on the loop theorem: Stallings’s example
- 30 Polyhedral interpolation theorems
- 31 Canonical configurations
- 32 Handle decompositions of tubes
- 33 PLH approximations of homeomorphisms, for regular neighborhoods of linear graphs in R3
- 34 PLH approximations of homeomorphisms, for polyhedral 3-cells
- 35 The Triangulation theorem
- 36 The Haupt?ermutung; tame imbedding