Rational Homotopy Stability for the Spaces of Algebraic Maps

New Zealand Journal of Mathematics (Online)

J. Lin

关键词: Sullivan-Haefliger model;    rational homotopy equivalence;    stability property;    nilpotent space.;   

学科分类：社会科学、人文和艺术（综合）

来源: University of Auckland * Department of Mathematics

【 摘 要 】

Let X be a path connected nilpotent (e.g. simply connected) complex algebraic variety with 2(X) a free abelian group of rank r. For a based algebraic map , we can assign it a multiple degreeunder the induced homomorphism . Letbe the space of based algebraic maps of degreefrominto X.Under some assumption we prove that the mapobtained by composingwithinduces rational homotopy equivalence up to some dimension, which tends to infinity as the degreegrows.

【 授权许可】

Unknown