English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

In this survey-research paper, we first introduce the theory of Smith classesof complexes with fixed-point free, periodic maps on them. These classes, whendefined for the deleted product of a simplicial complex $K$, are the same asthe embedding classes of $K$. Embedding classes, in turn, are generalizationsof the van Kampen obstruction class for embeddability of a $d$-dimensionalcomplex $K$ into the Euclidean $2d$-space. All of these concepts will beintroduced in simple terms. Second, we use the theory introduced in the firstpart to relate the embedding classes (or the special Smith classes) of the thecomplex $[3]*K$ with the embedding classes of $K$. Here $[3]*K$ is the join of$K$ with a set of three points. Specifically, we prove that if the $m$-thembedding class of $K$ is non-zero, then the $(m+2)$-nd embedding class of$[3]*K$ is non-zero. We also prove some of the consequences of this theorem forthe embeddability of $[3]*K$.

On the Smith classes, the van Kampen obstruction and embeddability of $[3]*K$