FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2005, VOLUME 11, NUMBER 4, PAGES 173-183

Degree-one maps of Seifert manifolds into the Poincaré homology sphere

A. A. Perfilyev

Abstract

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This paper is devoted to the Legrand--Wang--Zieschang problem of minimal (in the sense of degree-one maps) Seifert manifolds. The main result is that the set of all possible map degrees from a Seifert manifold to a manifold with a finite fundamental group whose base is a sphere or a torus depends only on residues of parameters of exceptional fibers of the Seifert manifold. The minimality of some Seifert manifolds is proved by using this theorem.

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Last modified: November 25, 2005