运算子上的广义微分形式与纤维化的代数模型
摘要
我们构造了广义微分形式的函子。在有限型幂零空间的情形下，它们确定了空间的弱同伦型。它们还以基本且自然的方式配备了 cup-i 积的作用。对于同伦意义下的交换代数（视为余纤维可分解的交换运算子分辨上的代数），我们利用广义微分形式证明了单纯映射的纤维的模型是该映射的代数模型的余纤维。We construct functors of generalized differential forms. In the case of nilpotent spaces of finite type, they determine the weak homotopy type of the spaces. Moreover they are equipped, in an elementary and natural way, with the action of cup-i products. Working with commutative algebras up to homotopy (viewed as algebras over a cofibrant resolution of the operad of commutative algebras), we show using these functors that the model of the fiber of a simplicial map is the cofiber of the algebraic model of this map.
引用
@article{arxiv.math/0202262,
title = {Formes differentielles generalisees sur une operade et modeles algebriques des fibrations},
author = {David Chataur},
journal= {arXiv preprint arXiv:math/0202262},
year = {2014}
}
备注
Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol2/agt-2-5.abs.html