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/

Zendy Plus

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

Zendy Tools

Zendy Open

We introduce non-acyclic $PGL_n(\mathbb{C})$-torsion of a 3-manifold withtoroidal boundary as an extension of J. Porti's $PGL_2(\mathbb{C})$-torsion,and present an explicit formula of the $PGL_n(\mathbb{C})$-torsion of a mappingtorus for a surface with punctures, by using the higher Teichm\"{u}ler theorydue to V. Fock and A. Goncharov. Our formula gives a concrete rational functionwhich represents the torsion function and comes from a concrete clustertransformation associated with the mapping class.

Torsion functions on moduli spaces in view of the cluster algebra