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

The equivariant bordism classification of manifolds with group actions is anessential subject in the study of transformation groups. We are interesting inthe action of 2-torus group $\mathbb{Z}_2^n$ and torus group $T^n$, and studythe equivariant bordism of 2-torus manifolds and unitary toric manifolds. Inthis paper, we give a new description of the group$\mathcal{Z}_n(\mathbb{Z}_2^n)$ of 2-torus manifolds, and determine thedimention of $\mathcal{Z}_n(\mathbb{Z}_2^n)$ as a $\mathbb{Z}_2$-vector space.With the help of toric topology, L\"u and Tan proved that the bordism groups$\mathcal{Z}_n(\mathbb{Z}_2^n)$ are generated by small covers. We will give anew proof to this result. These results can be generalized to the equivariantbordism of unitary toric manifolds, that is, we will give a new description ofthe group $\mathcal{Z}_n^U(T^n)$ of unitary torus manifolds, and prove that$\mathcal{Z}_n^U(T^n)$ can be generated by quasitoric manifolds withomniorientations.

Equivariant Bordism of 2-Torus Manifolds and Unitary Toric Manifolds