Glasnik Matematicki, Vol. 42, No.1 (2007), 109-116.

A COHOMOLOGICAL CHARACTERIZATION OF SHAPE DIMENSION FOR SOME CLASS OF SPACES

Jack Segal and Stanisaw Spiez

Department of Mathematics, University of Washington, Seattle, WA 98195, USA
e-mail: segal@math.washington.edu

Institute of Mathematics, Polish Academy of Sciences, Sniadeckich 8, P.O.B. 137, 00-950 Warszawa, Poland
e-mail: s.spiez@impan.gov.pl

Abstract.   It is known that if X is a metric compact space (compactum) with finite shape dimension sd(X) ≠ 2, then sd(X) is equal to the generalized coefficient of cyclicity c[X], equivalently sd(X × S1) = sd(X) + 1. In general, these equalities do not hold in the case of compacta with sd(X) = 2. In this paper we prove that if X is a regularly 1-movable connected pointed space with sd(X) = 2, then c[X] = 2.

2000 Mathematics Subject Classification.   54F45, 55P55.

Key words and phrases.   Shape dimension, regularly movable, cohomological dimension, Stallings-Swan theorem.

Full text (PDF) (free access)

DOI: 10.3336/gm.42.1.09

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