(Non-)contractible road spaces of trees

Contractible polyhedra in products of trees and absolute retracts in products of dendrites

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.

不可度量化流形与可缩性

Non-metrizable manifolds and contractibility

本文研究不可度量化流形与CW复形同伦等价的条件，通过实值映射稳定化性质证明多类不可度量化流形（含长射线切丛正部分、Prüfer曲面的某些开子流形）不是heCWc，并构造出不可度量化可缩的I型曲面。