Rad HAZU, Matematičke znanosti, Vol. 19 (2015), 143-149.

ELEMENTARY EXAMPLES OF ESSENTIAL PHANTOM MAPPINGS

Sibe Mardešić

Department of Mathematics, University of Zagreb, Bijenička cesta 30, 10 002 Zagreb, P.O. Box 335, Croatia
e-mail: smardes@math.hr

Abstract.   It is known that essential phantom mappings (of the second kind) between connected CW-complexes do exist. However, it appears that in the literature there are few explicit examples of such mappings. One usually finds descriptions of the domain and the codomain and an existence proof that the set of homotopy classes of mappings from the domain to the codomain is infinite. The purpose of the present paper is to describe some elementary examples of essential phantom mappings. The codomain is the n-sphere Sn, n ≥ 2, and the domain is the telescope Tn, associated with the sequence of copies of the canonical mapping f : Sn-1 → Sn-1 of odd degree p > 1. There are no essential phantom mappings whose codomain is the 1-sphere S1.

2010 Mathematics Subject Classification.   55S37.

Key words and phrases.   Homotopy, essential mapping, phantom mapping, telescope.

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