There Are No Essential Phantom Mappings from 1-dimensional CW-complexes

• Autorzy: Mardešić S.

Identyfikatory

DOI

10.4064/ba61-2-7

• Języki publikacji: EN

Abstrakty

EN

A phantom mapping h from a space Z to a space Y is a mapping whose restrictions to compact subsets are homotopic to constant mappings. If the mapping h is not homotopic to a constant mapping, one speaks of an essential phantom mapping. The definition of (essential) phantom pairs of mappings is analogous. In the study of phantom mappings (phantom pairs of mappings), of primary interest is the case when Z and Y are CW-complexes. In a previous paper it was shown that there are no essential phantom mappings (pairs of phantom mappings) between CW-complexes if dimY≤1. In the present paper it is shown that there are no essential phantom mappings between CW-complexes if dimZ≤1. In contrast, there exist essential phantom pairs of mappings between CW-complexes where dimZ=1 and dimY=2. Moreover, there exist essential phantom mappings with dimZ=dimY=1 where Y is a CW-complex, but Z is not.

Słowa kluczowe

EN

homotopy classification of mappings; phantom mappings; 1-dimensional CW-complexes

• Wydawca: Instytut Matematyczny PAN
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2013
• Tom: Vol. 61, no 2
• Strony: 141--147
• Opis fizyczny: Bibliogr. 5 poz.

Twórcy

autor

Mardešić S.

• Department of Mathematics University of Zagreb Bijenička cesta 30 10 002 Zagreb, P.O. Box 335, Croatia

Bibliografia

• [1] J. Dydak and S. Mardešić, A counterexample concerning products in the shape category, Fund. Math. 186 (2005), 39{54.
• [2] A. Hatcher, Algebraic Topology, Cambridge Univ. Press, Cambridge, 2002.
• [3] A. T. Lundell and S. Weingram, The Topology of CW-Complexes, Van Nostrand, New York, 1969.
• [4] S. Mardešić, There are no phantom pairs of mappings to 1-dimensional CW-complexes, Bull. Polish Acad. Sci. Math. 55 (2007), 365{371.
• [5] C. A. McGibbon, Phantom maps, Chapter 25 of Handbook of Algebraic Topology, I. M. James (ed.), Elsevier, Amsterdam, 1995, 1209{1257.