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

We have been interested in understanding the class of 7-dimensional closedand simply-connected manifolds in geometric and constructive ways. We haveconstructed explicit fold maps, which are higher dimensional versions of Morsefunctions, on some of the manifolds, previously.  The studies have been motivated by studies of {\it special generic} maps,higher dimensional versions of Morse functions on homotopy spheres with exactlytwo singular points, characterizing them topologically except $4$-dimensionalcases. The class contains canonical projections of unit spheres for example.  This class has been found to be interesting, restricting the topologies andthe differentiable structures of the manifolds strictly: Saeki, Sakuma andWrazidlo found explicit phenomena.  The present paper concerns fold maps on $7$-dimensional closed andsimply-connected spin manifolds whose integral cohomology rings are isomorphicto that of the product of the $2$-dimensional complex projective space and the$3$-dimensional sphere.

7-dimensional simply-connected spin manifolds whose integral cohomology  rings are isomorphic to that of ${\mathbb{C}P}^2 \times S^3$ admit round fold  maps