#### 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 *S*^{n}, *n* ≥ 2,
and the domain is the telescope *T*^{n}, associated with
the sequence of copies of the canonical mapping
*f* : *S*^{n-1} → *S*^{n-1}
of odd degree *p* > 1. There are no essential phantom mappings whose codomain
is the 1-sphere *S*^{1}.

**2010 Mathematics Subject Classification.**
55S37.

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

**Full text (PDF)** (free access)

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