Retractions of H-spaces

A retraction theorem for topological fundamental groups with application to the Hawaiian earring

A characterization of regular topological fundamental groups yields a `no retraction theorem' for spaces constructed in similar fashion to the Hawaiian earring.

关于retraction映射的数值不变量

On numerical invariants of retraction map

本文引入拓扑空间连续映射间的retraction概念，证明在retraction下同调维数、Lusternik-Schnirelmann范畴、拓扑复杂度等数值不变量满足相应不等式，并推广至新定义的不变量。

Equivariant control data and neighborhood deformation retractions

In this article we study Whitney (B) regular stratified spaces with the action of a compact Lie group $G$ which preserves the strata. We prove an equivariant submersion theorem and use it to show that such a $G$-stratified space carries a system of $G$-equivariant control data. As an application, we show that if $A \subset X$ is a closed $G$-stratified subspace which is a union of strata of $X$, then the inclusion $i : A \hookrightarrow X$ is a $G$-equivariant cofibration. In particular, this theorem applies whenever $X$ is a $G$-invariant analytic subspace of an analytic $G$-manifold $M$ and …

A Short Note on Mapping Cylinders

Given a homotopy equivalence f between two topological spaces we assemble well known pieces and unfold them into an explicit formula for a strong deformation retraction of the mapping cylinder of f onto its top.

Formality of spaces with Lusternik-Schnirelmann category 1

It is a well known fact that formal dg-algebras admit no non-trivial Massey products, while the converse fails. We prove that by restricting to dg-algebras whose induced product on cohomology is trivial, we do in fact get this converse. This allows us to prove that spaces of Lusternik-Schnirelmann category 1 are formal spaces.

收缩映射的截面范畴与模截面范畴

Sectional category versus module sectional category for retractive maps

构造满足 msecat(p)=2<secat(p)=3 的收缩映射，推翻 Carrasquel--Vera 猜想。