Geometric Topology and Shape Theory: Proceedings of a Conference held in Dubrovnik, Yugoslavia, Sept. 29 – Oct. 10, 1986

Fredric D. Ancel (auth.), Sibe Mardešić, Jack Segal (eds.)9780387184432, 0-387-18443-0

The aim of this international conference the third of its type was to survey recent developments in Geometric Topology and Shape Theory with an emphasis on their interaction. The volume contains original research papers and carefully selected survey of currently active areas. The main topics and themes represented by the papers of this volume include decomposition theory, cell-like mappings and CE-equivalent compacta, covering dimension versus cohomological dimension, ANR’s and LCn-compacta, homology manifolds, embeddings of continua into manifolds, complement theorems in shape theory, approximate fibrations and shape fibrations, fibered shape, exact homologies and strong shape theory.

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Table of contents :
An alternative proof of M. Brown’s theorem on inverse sequences of near homeomorphisms….Pages 1-2
Strong homology theories….Pages 3-29
Borsuk fixed point theorem for multi-valued maps….Pages 30-37
Improving categorical coverings of spaces….Pages 38-42
The intimate connections among decomposition theory, embedding theory, and manifold structure theory….Pages 43-47
On resolutions of LC n -compacta….Pages 48-59
Infinite-dimensional compacta with finite cohomological dimension modulo p….Pages 60-64
Sheaves that are locally constant with applications to homology manifolds….Pages 65-87
UV k -equivalent compacta….Pages 88-114
Covering maps in top N ….Pages 115-124
Embedding of continua….Pages 125-130
Using solenoids in the study of the Stone-Čech compactification….Pages 131-147
The alexander-pontryagin duality theorem for coherent homology and cohomology with coefficients in sheaves of modules….Pages 148-163
On exact homology….Pages 164-182
Geometric category and Lusternik-Schnirelmann category….Pages 183-192
On the homology of function spaces….Pages 193-201
On shape theory with compact supports….Pages 202-211
Complement theorems in shape theory, II….Pages 212-220
The continuity axiom and the Čech homology….Pages 221-239
Fiber shape theory, shape fibrations and movability of maps….Pages 240-252
Some open questions in geometric topology and shape theory….Pages 253-255