On T-modifications of mappings into surfaces

• Autorzy: Karno Z.
• Języki publikacji: EN

Abstrakty

EN

It is shown that if X is a compact 2-dimensional polyhedron and if f is a mapping of X to a surface M, then f x id[sub Ik] (f x id[sub Sk], respectively) is essential for every [k is greater than or equal to 0] if and only if each T-modification of f is essential.

Słowa kluczowe

EN

algebraic topology; essential mapping; homotopy groups; manifolds and cell complexes; modification; polyhedra; product; sets of homotopy classes; surface

PL

grupy homotopii; powierzchnia; produkt; rozmaitości topologiczne; rzutowanie; topologia algebraiczna; topological manifolds; wielościan

• Wydawca: Instytut Matematyczny PAN
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 1998
• Tom: Vol. 46, no. 4
• Strony: 345--350
• Opis fizyczny: Bibliogr. 12 poz.,

Twórcy

autor

Karno Z.

• Institute of Mathematics, Polish Academy of Sciences, Śniadeckich 8, 00-950 Warszawa, Poland
• Institute of Mathematics, University of Białystok, Akademicka 2, 15-267 Białystok 1, Poland

Bibliografia

• [1] J. Grispolakis, E. D. Туmchatyn, On confluent mappings and essential mappings - a survey, Rocky Mountain J. Math., 11 (1981) 131-153.
• [2] J. Krasinkiewicz, Essential mappings onto products of manifolds, in: Geometric and Algebraic Topology, Banach Center Publication 18, PWN, Warszawa (1986) 377-406.
• [3] Н. Hopf, Über wesentliche und unwesentliche Abbildungen von Komplexen, Recueil Math. de Moscou 1930, 53-62.
• [4] Z. Karnо, On ω-essential mappings onto manifolds, Fund. Math., 137 (1991) 97-105.
• [5] Z. Karnо, On a theorem of P. S. Aleksandrov, Collog. Math., 72 (1997) 39-51.
• [6] Z. Karnо, Stably essential mappings onto disks, Acta Math. Hungar., 80 (1998) 289-301.
• [7] Z. Kаrno, Stably essential mappings onto spheres, Acta Math. Hungar., to be published.
• [8] W. Holsztyński, Universality of the product mapping onto products of In and snake-lake spaces, Fund. Math., 64 (1969) 147-155.
• [9] K. Мorita, Cech cohomology and covering dimension for topological spaces, Fund. Math., 87 (1.975) 31-52.
• [10] Z. Karno, Remarks оn essential mappings onto surfaces, in: Topology with Applications (Szekszárd, Hungary, 1993), Bоlуai Society Mathematical Studies, 4 (1995) 275-280.
• [11] Z. Karno, Some еxamples of essential mnappings onto surfaces, Bull Pol. Ac.: Math., 42 (1994) 271-276.
• [12] Z. Karno, On a duality between membranes and separators, Bull. Pol. Ac.: Math., 41 (1993) 103-108.