树的积中的收缩多面体与枝晶的积中的绝对收缩核
Contractible polyhedra in products of trees and absolute retracts in products of dendrites
摘要：
我们证明了一个紧的n-多面体PL嵌入n棵树的乘积当且仅当它坍缩到一个（n-1）-多面体上。如果n-多面体是可收缩的并且n \ne 3（或者n=3并且Andrews-Curtis猜想成立），则可以假设树的乘积塌陷到嵌入的图像上。相反，存在一个2维紧致绝对收缩核X，使得X \times I^k不嵌入任何2+k个枝晶的乘积中。
英文摘要：
We show that a compact n-polyhedron PL embeds in a product of n trees if and only if it collapses onto an (n-1)-polyhedron. If the n-polyhedron is contractible and n\ne 3 (or n=3 and the Andrews-Curtis Conjecture holds), the product of trees may be assumed to collapse onto the image of the embedding. In contrast, there exists a 2-dimensional compact absolute retract X such that X\times I^k does not embed in any product of 2+k dendrites for each k.
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