Geometric Topology

1st Edition - January 1, 1979
Editor: James C. Cantrell
Language: English
eBook ISBN:
9 7 8 - 1 - 4 8 3 2 - 7 1 3 1 - 6

Geometric Topology contains the proceedings of the 1977 Georgia Topology Conference, held at the University of Georgia on August 1977. The book is comprised of contributions from… Read more

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Geometric Topology contains the proceedings of the 1977 Georgia Topology Conference, held at the University of Georgia on August 1977. 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 topology, and miscellaneous problems. Subjects discussed under these sections include local spanning missing loops, the structure of generalized manifolds having nonmanifold set of trivial dimension, universal open principal fibrations, and how to build a flexible polyhedral surface. Topologists, geometers, and mathematicians will find the book very interesting and insightful.

Contributors

Preface

Part I Low Dimensional Manifolds

A Decomposition of S3 with a Null Sequence of Cellular Arcs

Special Representations for 3-Manifolds

Shrinking Countable Decompositions of E3 into Points and Tame Cells

Local Spanning Missing Loops

A Problem of Rushing

An Additive Index Theorem for Certain Wildly Embedded Arcs and Curves

Seifert Fibered Spaces in 3-Manifolds

On Exotic Homotopy Equivalences of 3-Manifolds

Eight Faces of the Poincare Homology 3-Sphere

Decomposing Analytic Surfaces

Heegaard Diagrams for Closed 4-Manifolds

Decompositions of E3 with Countably Many Non-Degenerate Elements

Decompositions of E3 into Cellular Sets

Part II Topology of Manifolds

The Structure of Generalized Manifolds Having Nonmanifold Set of Trivial Dimension

Embeddings and Immersions of Four Dimensional Manifolds in R6

General Position Maps for Topological Manifolds

The Equivariant Surgery Problem for Involutions

The Degree of a Branched Covering of a Sphere

A Universal 5-Manifold with Respect to Simplicial Triangulations

On πi DIFF Mn

Construction of Surgery Problems

Wild Embeddings of Piecewise Linear Manifolds in Codimension Two

Foliations and Monoids of Embeddings

On the Topology of Nonisolated Singularities

Approximating CAT CE Maps by CAT Homeomorphisms

On Complexes That Are Lipschitz Manifolds

Isometries of Inner Product Spaces and Their Geometric Applications

Hyperbolic Geometry and Homeomorphisms

K2 and Diffeomorphisms of Two and Three Dimensional Manifolds

Part III Shape Theory And Infinite Dimensional Topology

Concordances of Hilbert Cube Manifolds and Tubular Neighborhoods of Finite-Dimensional Manifolds

Universal Open Principal Fibrations

Compacta with the Homotopy Type of Finite Complexes

Manifolds Modeled on the Direct Limit of Hilbert Cubes

Concordance Classes of Free Actions of Compact Lie Groups on Infinite Dimensional Manifolds

Cell-Like Maps, Approximate Fibrations and Shape Fibrations

A Weak Flattening Criterion for Compacta in 4-Space

Based-Free Actions of Finite Groups on Hilbert Cubes with Absolute Retract Orbit Spaces are Conjugate

Part IV Miscellaneous Problems

How to Build a Flexible Polyhedral Surface

A Short List of Problems

Some Borsuk-Ulam Type Theorems